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Theorem pm2.52 590
Description: Theorem *2.52 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
pm2.52 (¬ (𝜑𝜓) → (¬ 𝜑 → ¬ 𝜓))

Proof of Theorem pm2.52
StepHypRef Expression
1 pm2.21 555 . . 3 𝜑 → (𝜑𝜓))
21pm2.24d 560 . 2 𝜑 → (¬ (𝜑𝜓) → ¬ 𝜓))
32com12 30 1 (¬ (𝜑𝜓) → (¬ 𝜑 → ¬ 𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in2 553
This theorem is referenced by:  pm2.521dc  773
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