Theorem pm2.21fal 1418

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 625	1 |- ( ph -> F. )

Syntax hints:   -. wn 3   -> wi 4   F. wfal 1403

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in2 620

This theorem is referenced by:  genpdisj  7786  suplocexprlemdisj  7983  suplocexprlemub  7986  suplocsrlem  8071  recvguniqlem  11617  resqrexlemoverl  11644  leabs  11697  climge0  11948  isprm5lem  12776  dedekindeulemeu  15416  dedekindicclemeu  15425  usgr1vr  16172  pw1nct  16708