Theorem mpanl2 411

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 298	. 2 |- ( ph -> ( ph /\ ps ) )
3		mpanl2.2	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
4	2, 3	sylan 267	1 |- ( ( ph /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem is referenced by:  mpanr1  413  mp3an2  1220  reuss  3218  tfri3  5953  prarloclemarch2  6517  prarloclemlt  6591  prsradd  6870  pitonnlem2  6923  axcnre  6955  muleqadd  7649  divdivap2  7700  addltmul  8161