Theorem syl3anr2 1291

Description: A syllogism inference. (Contributed by NM, 1-Aug-2007.)

Hypotheses

Ref	Expression
syl3anr2.1	|- ( ph -> th )
syl3anr2.2	|- ( ( ch /\ ( ps /\ th /\ ta ) ) -> et )

Assertion

Ref	Expression
syl3anr2	|- ( ( ch /\ ( ps /\ ph /\ ta ) ) -> et )

Proof of Theorem syl3anr2

Step	Hyp	Ref	Expression
1		syl3anr2.1	. . 3 |- ( ph -> th )
2		syl3anr2.2	. . . 4 |- ( ( ch /\ ( ps /\ th /\ ta ) ) -> et )
3	2	ancoms 268	. . 3 |- ( ( ( ps /\ th /\ ta ) /\ ch ) -> et )
4	1, 3	syl3anl2 1287	. 2 |- ( ( ( ps /\ ph /\ ta ) /\ ch ) -> et )
5	4	ancoms 268	1 |- ( ( ch /\ ( ps /\ ph /\ ta ) ) -> et )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 978

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 980

This theorem is referenced by:  mulgsubdir  13029