What the Maharsha questioned, that the kal vachomer (a fortiori) argument is flawed, because the frogs were not commanded with the mitzvah of "and live by them" – indeed, it is so, and if the desire of Hananiah, Mishael, and Azariah was to learn from them the very obligation of self-sacrifice for the sanctification of Hashem's name, it would indeed be a flawed kal vachomer, as the Maharsha's question implies, for one cannot learn self-sacrifice from them, since they are not commanded with "and live by them," it is easier to obligate them in the loss of their lives. However, in truth, Hananiah, Mishael, and Azariah did not seek to learn the obligation of self-sacrifice from the frogs, nor any obligation or stringency at all; rather, they sought to learn understanding from them – the understanding of the true meaning of the concept of 'life.' The frogs understood this concept deeply, and this is what Hananiah, Mishael, and Azariah sought to learn. They reasoned with their own kal vachomer and said: If these, who are not commanded regarding the sanctification of Hashem's name, nevertheless recognized that true life is in the sanctification of His name and in doing His will, and that the drive for life should be directed towards this – we, who are commanded regarding the sanctification of Hashem's name, all the more so should recognize this. And for this learning, there is no place for the Maharsha's refutation, because the absence of the command "and live by them" for the frogs does not influence or sway this understanding of the meaning of life that Hananiah, Mishael, and Azariah wanted to learn from them.

The question of the Sha'agat Aryeh also has no place according to the words of the Maharil Diskin, since in his opinion there was no commandment for the frogs to enter the ovens, contrary to the opinion of the Sha'agat Aryeh.

And even the Tosafot's resolution now shines in a new light, as they explained that Nebuchadnezzar's image was not actual idolatry but an idol he made for his own honor. Therefore, Hananiah, Mishael, and Azariah needed to learn self-sacrifice from the frogs – and with our words, we can fully understand the nature and depth of this learning that they derived from them. The aspiration to act and bring about the sanctification of Hashem's name must be rooted in the initial and primary place of life – in the life drive itself. This is the true and correct expression of this drive, the correct way to bring it from potential to actual – not a drive for preserving and protecting physical life, but a yearning and longing to achieve the purpose of life, which is the sanctification of Hashem's name. This is what Hananiah, Mishael, and Azariah learned from the frogs, and once they reached this understanding, they resolved to sacrifice themselves for the sanctification of Hashem's name.