Theorem mp3anr3 917

Description: An inference based on modus ponens.

Hypotheses

Ref	Expression
mp3anr3.1	|- th
mp3anr3.2	|- ((ph /\ (ps /\ ch /\ th)) -> ta)

Assertion

Ref	Expression
mp3anr3	|- ((ph /\ (ps /\ ch)) -> ta)

Proof of Theorem mp3anr3

Step	Hyp	Ref	Expression
1		mp3anr3.1	. . 3 |- th
2		mp3anr3.2	. . . 4 |- ((ph /\ (ps /\ ch /\ th)) -> ta)
3	2	ancoms 438	. . 3 |- (((ps /\ ch /\ th) /\ ph) -> ta)
4	1, 3	mp3anl3 914	. 2 |- (((ps /\ ch) /\ ph) -> ta)
5	4	ancoms 438	1 |- ((ph /\ (ps /\ ch)) -> ta)

Syntax hints:   -> wi 3   /\ wa 223   /\ w3a 777

This theorem is referenced by:  blocnilem 8460

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 779

Copyright terms: Public domain