Theorem sylanr1 396

Description: A syllogism inference. (Contributed by NM, 9-Apr-2005.)

Hypotheses

Ref	Expression
sylanr1.1	|- ( ph -> ch )
sylanr1.2	|- ( ( ps /\ ( ch /\ th ) ) -> ta )

Assertion

Ref	Expression
sylanr1	|- ( ( ps /\ ( ph /\ th ) ) -> ta )

Proof of Theorem sylanr1

Step	Hyp	Ref	Expression
1		sylanr1.1	. . 3 |- ( ph -> ch )
2	1	anim1i 333	. 2 |- ( ( ph /\ th ) -> ( ch /\ th ) )
3		sylanr1.2	. 2 |- ( ( ps /\ ( ch /\ th ) ) -> ta )
4	2, 3	sylan2 280	1 |- ( ( ps /\ ( ph /\ th ) ) -> ta )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem is referenced by:  adantrll  467  adantrlr  468