Theorem pm2.61ii 157

Description: Inference eliminating two antecedents. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.)

Hypotheses

Ref	Expression
pm2.61ii.1	|- (-. ph -> (-. ps -> ch))
pm2.61ii.2	|- (ph -> ch)
pm2.61ii.3	|- (ps -> ch)

Assertion

Ref	Expression
pm2.61ii	|- ch

Proof of Theorem pm2.61ii

Step	Hyp	Ref	Expression
1		pm2.61ii.2	. 2 |- (ph -> ch)
2		pm2.61ii.1	. . 3 |- (-. ph -> (-. ps -> ch))
3		pm2.61ii.3	. . 3 |- (ps -> ch)
4	2, 3	pm2.61d2 152	. 2 |- (-. ph -> ch)
5	1, 4	pm2.61i 156	1 |- 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:  pm2.61iii  159  hbae  1953  sbequi  2059  sbcom  2089  sbcom2  2114  hbae-o  2153  hbequid  2160  ax17eq  2183  ax17el  2189