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Theorem pm2.21fal 1280
Description: If a wff and its negation are provable, then falsum is provable. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypotheses
Ref Expression
pm2.21fal.1 (𝜑𝜓)
pm2.21fal.2 (𝜑 → ¬ 𝜓)
Assertion
Ref Expression
pm2.21fal (𝜑 → ⊥)

Proof of Theorem pm2.21fal
StepHypRef Expression
1 pm2.21fal.1 . 2 (𝜑𝜓)
2 pm2.21fal.2 . 2 (𝜑 → ¬ 𝜓)
31, 2pm2.21dd 560 1 (𝜑 → ⊥)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wfal 1264
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in2 555
This theorem is referenced by:  genpdisj  6678  recvguniqlem  9813  resqrexlemoverl  9840  leabs  9893  climge0  10068
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