Theorem pm2.61an1 364

Description: Elimination of an antecedent.

Hypotheses

Ref	Expression
pm2.61an1.1	|- ((ph /\ ps) -> ch)
pm2.61an1.2	|- ((-. ph /\ ps) -> ch)

Assertion

Ref	Expression
pm2.61an1	|- (ps -> ch)

Proof of Theorem pm2.61an1

Step	Hyp	Ref	Expression
1		pm2.61an1.1	. . 3 |- ((ph /\ ps) -> ch)
2	1	exp 291	. 2 |- (ph -> (ps -> ch))
3		pm2.61an1.2	. . 3 |- ((-. ph /\ ps) -> ch)
4	3	exp 291	. 2 |- (-. ph -> (ps -> ch))
5	2, 4	pm2.61i 110	1 |- (ps -> ch)

Syntax hints:  -. wn 1   -> wi 2   /\ wa 196

This theorem is referenced by:  4cases 565  findsg 2398  tfindsg 2402

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org