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Theorem pm2.21fal 1351
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 609 1 (𝜑 → ⊥)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wfal 1336
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in2 604
This theorem is referenced by:  genpdisj  7343  suplocexprlemdisj  7540  suplocexprlemub  7543  suplocsrlem  7628  recvguniqlem  10778  resqrexlemoverl  10805  leabs  10858  climge0  11106  dedekindeulemeu  12783  dedekindicclemeu  12792  pw1nct  13303
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