Theorem pm2.21fal 1384

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

Step	Hyp	Ref	Expression
1		pm2.21fal.1	. 2 |- ( ph -> ps )
2		pm2.21fal.2	. 2 |- ( ph -> -. ps )
3	1, 2	pm2.21dd 621	1 |- ( ph -> F. )

Syntax hints:   -. wn 3   -> wi 4   F. wfal 1369

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in2 616

This theorem is referenced by:  genpdisj  7541  suplocexprlemdisj  7738  suplocexprlemub  7741  suplocsrlem  7826  recvguniqlem  11022  resqrexlemoverl  11049  leabs  11102  climge0  11352  isprm5lem  12160  dedekindeulemeu  14503  dedekindicclemeu  14512  pw1nct  15156