Theorem mpd3an3 1278

Description: An inference based on modus ponens. (Contributed by NM, 8-Nov-2007.)

Hypotheses

Ref	Expression
mpd3an3.2	|- ((ph /\ ps) -> ch)
mpd3an3.3	|- ((ph /\ ps /\ ch) -> th)

Assertion

Ref	Expression
mpd3an3	|- ((ph /\ ps) -> th)

Proof of Theorem mpd3an3

Step	Hyp	Ref	Expression
1		mpd3an3.2	. 2 |- ((ph /\ ps) -> ch)
2		mpd3an3.3	. . 3 |- ((ph /\ ps /\ ch) -> th)
3	2	3expa 1151	. 2 |- (((ph /\ ps) /\ ch) -> th)
4	1, 3	mpdan 649	1 |- ((ph /\ ps) -> th)

Syntax hints:   -> wi 4   /\ wa 358   /\ w3a 934

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  df-3an 936

This theorem is referenced by:  nnsucelr  4429  cupvalg  5813  ovcross  5846  pmvalg  6011  enadj  6061  ovmuc  6131  ovce  6173  addlecncs  6210  leconnnc  6219  ncslesuc  6268