Theorem pm2.21d 98

Description: A contradiction implies anything. Deduction from pm2.21 100. (Contributed by NM, 10-Feb-1996.)

Hypothesis

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

Assertion

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

Proof of Theorem pm2.21d

Step	Hyp	Ref	Expression
1		pm2.21d.1	. . 3 |- (ph -> -. ps)
2	1	a1d 22	. 2 |- (ph -> (-. ch -> -. ps))
3	2	con4d 97	1 |- (ph -> (ps -> 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:  pm2.21dd  99  pm2.21  100  2falsed  340  pm5.14  856  ecase2d  906  prlem1  928  sbc2or  3055  eq0rdv  3586  rzal  3652  ssofss  4077  tfinltfin  4502  clos1nrel  5887  nchoicelem12  6301