Theorem pm2.21fal 1417

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 1402

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

This theorem is referenced by:  genpdisj  7743  suplocexprlemdisj  7940  suplocexprlemub  7943  suplocsrlem  8028  recvguniqlem  11572  resqrexlemoverl  11599  leabs  11652  climge0  11903  isprm5lem  12731  dedekindeulemeu  15365  dedekindicclemeu  15374  usgr1vr  16118  pw1nct  16655