Theorem mpanl2 662

Description: An inference based on modus ponens. (Contributed by NM, 16-Aug-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Hypotheses

Ref	Expression
mpanl2.1	|- ps
mpanl2.2	|- (((ph /\ ps) /\ ch) -> th)

Assertion

Ref	Expression
mpanl2	|- ((ph /\ ch) -> th)

Proof of Theorem mpanl2

Step	Hyp	Ref	Expression
1		mpanl2.1	. . 3 |- ps
2	1	jctr 526	. 2 |- (ph -> (ph /\ ps))
3		mpanl2.2	. 2 |- (((ph /\ ps) /\ ch) -> th)
4	2, 3	sylan 457	1 |- ((ph /\ ch) -> th)

This proof depends on syntax axioms:   -> wi 4   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is used by:  mpanr1  664  mp3an2  1265  reuss  3537  vfinncsp  4555