Deductive Argument In Plato's Apology

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One of the argument found in Plato’s Apology is that during the trial, Socrates had tried to defend himself in front of the judges and spoke, “If I disobeyed the oracle because I was afraid of death, then I should be fancying that I was wise when I was not wise”. This is an example of a Deductive Argument because it has a hypothetical syllogism which consist of having a conditional statement for both its premises in this case. More interestingly in this argument, it consists of pure hypothetical syllogism due to the fact that both statements are conditional. Based on the information given in this form of argument, I believed that this is considered to be an invalid argument because the conclusion does not necessarily follow both premises as

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