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Theorem frege33 36949
Description: If 𝜑 or 𝜓 takes place, then 𝜓 or 𝜑 takes place. Identical to con1 141. Proposition 33 of [Frege1879] p. 44. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege33 ((¬ 𝜑𝜓) → (¬ 𝜓𝜑))

Proof of Theorem frege33
StepHypRef Expression
1 ax-frege28 36943 . 2 ((¬ 𝜑𝜓) → (¬ 𝜓 → ¬ ¬ 𝜑))
2 frege32 36948 . 2 (((¬ 𝜑𝜓) → (¬ 𝜓 → ¬ ¬ 𝜑)) → ((¬ 𝜑𝜓) → (¬ 𝜓𝜑)))
31, 2ax-mp 5 1 ((¬ 𝜑𝜓) → (¬ 𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 36903  ax-frege2 36904  ax-frege28 36943  ax-frege31 36947
This theorem is referenced by:  frege34  36950  frege46  36963
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