MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm2.21fal Structured version   Unicode version

Theorem pm2.21fal 1393
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 174 1  |-  ( ph  -> F.  )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   F. wfal 1375
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  dihglblem6  35294
  Copyright terms: Public domain W3C validator