Theorem mpanl12 663

Description: An inference based on modus ponens. (Contributed by NM, 13-Jul-2005.)

Hypotheses

Ref	Expression
mpanl12.1	|- ph
mpanl12.2	|- ps
mpanl12.3	|- (((ph /\ ps) /\ ch) -> th)

Assertion

Ref	Expression
mpanl12	|- (ch -> th)

Proof of Theorem mpanl12

Step	Hyp	Ref	Expression
1		mpanl12.2	. 2 |- ps
2		mpanl12.1	. . 3 |- ph
3		mpanl12.3	. . 3 |- (((ph /\ ps) /\ ch) -> th)
4	2, 3	mpanl1 661	. 2 |- ((ps /\ ch) -> th)
5	1, 4	mpan 651	1 |- (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:  reuun1  3538  funprg  5150  mucnc  6132