Theorem mpd3an23 918

Description: An inference based on modus ponens.

Hypotheses

Ref	Expression
mpd3an23.1	|- (ph -> ps)
mpd3an23.2	|- (ph -> ch)
mpd3an23.3	|- ((ph /\ ps /\ ch) -> th)

Assertion

Ref	Expression
mpd3an23	|- (ph -> th)

Proof of Theorem mpd3an23

Step	Hyp	Ref	Expression
1		mpd3an23.3	. 2 |- ((ph /\ ps /\ ch) -> th)
2		id 59	. 2 |- (ph -> ph)
3		mpd3an23.1	. 2 |- (ph -> ps)
4		mpd3an23.2	. 2 |- (ph -> ch)
5	1, 2, 3, 4	syl3anc 858	1 |- (ph -> th)

Syntax hints:   -> wi 3   /\ w3a 775

This theorem is referenced by:  euuni 2881  qbtwnxr 6279  grpinvid 8074  shftefif1olem 8741  chsot 9589

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225  df-3an 777

Copyright terms: Public domain