Theorem pm2.21dd 99

Description: A contradiction implies anything. Deduction from pm2.21 100. (Contributed by Mario Carneiro, 9-Feb-2017.)

Hypotheses

Ref	Expression
pm2.21dd.1	|- (ph -> ps)
pm2.21dd.2	|- (ph -> -. ps)

Assertion

Ref	Expression
pm2.21dd	|- (ph -> ch)

Proof of Theorem pm2.21dd

Step	Hyp	Ref	Expression
1		pm2.21dd.1	. 2 |- (ph -> ps)
2		pm2.21dd.2	. . 3 |- (ph -> -. ps)
3	2	pm2.21d 98	. 2 |- (ph -> (ps -> ch))
4	1, 3	mpd 14	1 |- (ph -> ch)

Syntax hints:  -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  pm2.21fal  1335  pm2.21ddne  2591