Theorem pm2.21dd 625

Description: A contradiction implies anything. Deduction from pm2.21 622. (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 624	. 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-mp 5  ax-1 6  ax-2 7  ax-in2 620

This theorem is referenced by:  pm2.21fal  1417  pm2.21ddne  2485  ordtriexmidlem  4617  ordtri2or2exmidlem  4624  onsucelsucexmidlem  4627  wetriext  4675  reg3exmidlemwe  4677  nntr2  6671  nnm00  6698  phpm  7052  fidifsnen  7057  dif1enen  7069  infnfi  7084  en2eqpr  7099  pr2cv1  7400  aptiprleml  7859  aptiprlemu  7860  uzdisj  10328  nn0disj  10373  zsupcllemex  10490  addmodlteq  10660  frec2uzlt2d  10666  iseqf1olemab  10764  iseqf1olemmo  10767  hashennnuni  11041  hashfiv01gt1  11044  xrmaxiflemab  11808  xrmaxiflemlub  11809  xrmaxltsup  11819  xrbdtri  11837  divalglemeunn  12483  divalglemeuneg  12485  ennnfonelemk  13022  cnplimclemle  15394  efltlemlt  15500  trilpolemlt1  16648  neapmkvlem  16674