Theorem pm2.21dd 550

Description: A contradiction implies anything. Deduction from pm2.21 547. (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 549	. 2 |- ( ph -> ( ps -> ch ) )
4	1, 3	mpd 13	1 |- ( ph -> ch )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in2 545

This theorem is referenced by:  pm2.21fal  1264  pm2.21ddne  2288  ordtriexmidlem  4245  ordtri2or2exmidlem  4251  onsucelsucexmidlem  4254  wetriext  4301  reg3exmidlemwe  4303  nnm00  6102  phpm  6327  fidifsnen  6331  aptiprleml  6737  aptiprlemu  6738  uzdisj  8955  nn0disj  8995  frec2uzlt2d  9190