Theorem mpanl2 426

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 308	. 2 |- ( ph -> ( ph /\ ps ) )
3		mpanl2.2	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
4	2, 3	sylan 277	1 |- ( ( ph /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem is referenced by:  mpanr1  428  mp3an2  1261  reuss  3280  tfri3  6132  prarloclemarch2  6978  prarloclemlt  7052  prsradd  7331  pitonnlem2  7384  axcnre  7416  muleqadd  8137  divdivap2  8191  addltmul  8652