Theorem mpd3an3 1274

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 1143	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
4	1, 3	mpdan 412	1 |- ( ( ph /\ ps ) -> th )

Syntax hints:   -> wi 4   /\ wa 102   /\ w3a 924

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 depends on definitions:  df-bi 115  df-3an 926

This theorem is referenced by:  stoic2b  1364  elovmpt2  5845  oav  6215  omv  6216  oeiv  6217  f1oeng  6472  mulpipq2  6928  ltrnqg  6977  genipv  7066  subval  7672  subap0  8116  fzrevral3  9517  fzoval  9555  subsq2  10058  bcval  10153  dvdsmul1  11092  dvdsmul2  11093  gcdval  11225  eucalgval2  11309  setsvalg  11519  cncfval  11583