Theorem syl3anl2 1184

Description: A syllogism inference. (Contributed by NM, 24-Feb-2005.)

Hypotheses

Ref	Expression
syl3anl2.1	|- ( ph -> ch )
syl3anl2.2	|- ( ( ( ps /\ ch /\ th ) /\ ta ) -> et )

Assertion

Ref	Expression
syl3anl2	|- ( ( ( ps /\ ph /\ th ) /\ ta ) -> et )

Proof of Theorem syl3anl2

Step	Hyp	Ref	Expression
1		syl3anl2.1	. . 3 |- ( ph -> ch )
2		syl3anl2.2	. . . 4 |- ( ( ( ps /\ ch /\ th ) /\ ta ) -> et )
3	2	ex 108	. . 3 |- ( ( ps /\ ch /\ th ) -> ( ta -> et ) )
4	1, 3	syl3an2 1169	. 2 |- ( ( ps /\ ph /\ th ) -> ( ta -> et ) )
5	4	imp 115	1 |- ( ( ( ps /\ ph /\ th ) /\ ta ) -> et )

Syntax hints:   -> wi 4   /\ wa 97   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  syl3anr2  1188