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Theorem frege36 40527
Description: The case in which 𝜓 is denied, ¬ 𝜑 is affirmed, and 𝜑 is affirmed does not occur. If 𝜑 occurs, then (at least) one of the two, 𝜑 or 𝜓, takes place (no matter what 𝜓 might be). Identical to pm2.24 124. Proposition 36 of [Frege1879] p. 45. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege36 (𝜑 → (¬ 𝜑𝜓))

Proof of Theorem frege36
StepHypRef Expression
1 ax-frege1 40478 . 2 (𝜑 → (¬ 𝜓𝜑))
2 frege34 40525 . 2 ((𝜑 → (¬ 𝜓𝜑)) → (𝜑 → (¬ 𝜑𝜓)))
31, 2ax-mp 5 1 (𝜑 → (¬ 𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 40478  ax-frege2 40479  ax-frege28 40518  ax-frege31 40522
This theorem is referenced by:  frege37  40528  frege38  40529  frege83  40634
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