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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  |-  ( ph  ->  ps )
pm2.21fal.2  |-  ( ph  ->  -.  ps )
Assertion
Ref Expression
pm2.21fal  |-  ( ph  -> F.  )

Proof of Theorem pm2.21fal
StepHypRef Expression
1 pm2.21fal.1 . 2  |-  ( ph  ->  ps )
2 pm2.21fal.2 . 2  |-  ( ph  ->  -.  ps )
31, 2pm2.21dd 560 1  |-  ( ph  -> F.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   F. 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  6679  recvguniqlem  9821  resqrexlemoverl  9848  leabs  9901  climge0  10076
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