Theorem sylanr2 634

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

Hypotheses

Ref	Expression
sylanr2.1	|- (ph -> th)
sylanr2.2	|- ((ps /\ (ch /\ th)) -> ta)

Assertion

Ref	Expression
sylanr2	|- ((ps /\ (ch /\ ph)) -> ta)

Proof of Theorem sylanr2

Step	Hyp	Ref	Expression
1		sylanr2.1	. . 3 |- (ph -> th)
2	1	anim2i 552	. 2 |- ((ch /\ ph) -> (ch /\ th))
3		sylanr2.2	. 2 |- ((ps /\ (ch /\ th)) -> ta)
4	2, 3	sylan2 460	1 |- ((ps /\ (ch /\ ph)) -> ta)

Syntax hints:   -> wi 4   /\ wa 358

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

This theorem is referenced by:  adantrrl  704  adantrrr  705