Theorem mpanl2 435

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 315	. 2 |- ( ph -> ( ph /\ ps ) )
3		mpanl2.2	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
4	2, 3	sylan 283	1 |- ( ( ph /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  mpanr1  437  mp3an2  1325  reuss  3418  tfri3  6370  prarloclemarch2  7420  prarloclemlt  7494  prsradd  7787  map2psrprg  7806  pitonnlem2  7848  axcnre  7882  muleqadd  8627  divdivap2  8683  addltmul  9157