Theorem mpd3an23 1279

Description: An inference based on modus ponens. (Contributed by NM, 4-Dec-2006.)

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		id 19	. 2 |- (ph -> ph)
2		mpd3an23.1	. 2 |- (ph -> ps)
3		mpd3an23.2	. 2 |- (ph -> ch)
4		mpd3an23.3	. 2 |- ((ph /\ ps /\ ch) -> th)
5	1, 2, 3, 4	syl3anc 1182	1 |- (ph -> th)

Syntax hints:   -> wi 4   /\ 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: (None)