Theorem pm2.21fal 1422

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 629	1 |- ( ph -> F. )

This proof depends on syntax axioms:   -. wn 3   -> wi 4   F. wfal 1407

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in2 624

This theorem is used by:  genpdisj  7896  suplocexprlemdisj  8093  suplocexprlemub  8096  suplocsrlem  8181  recvguniqlem  11782  resqrexlemoverl  11809  leabs  11862  climge0  12116  isprm5lem  12945  dedekindeulemeu  15848  dedekindicclemeu  15857  usgr1vr  16694  pw1nct  17238