Theorem mpanl1 661

Description: An inference based on modus ponens. (Contributed by NM, 16-Aug-1994.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)

Hypotheses

Ref	Expression
mpanl1.1	|- ph
mpanl1.2	|- (((ph /\ ps) /\ ch) -> th)

Assertion

Ref	Expression
mpanl1	|- ((ps /\ ch) -> th)

Proof of Theorem mpanl1

Step	Hyp	Ref	Expression
1		mpanl1.1	. . 3 |- ph
2	1	jctl 525	. 2 |- (ps -> (ph /\ ps))
3		mpanl1.2	. 2 |- (((ph /\ ps) /\ ch) -> th)
4	2, 3	sylan 457	1 |- ((ps /\ ch) -> th)

Syntax hints:   -> wi 4   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  mpanl12  663