Theorem sylan2i 636

Description: A syllogism inference. (Contributed by NM, 1-Aug-1994.)

Hypotheses

Ref	Expression
sylan2i.1	|- (ph -> th)
sylan2i.2	|- (ps -> ((ch /\ th) -> ta))

Assertion

Ref	Expression
sylan2i	|- (ps -> ((ch /\ ph) -> ta))

Proof of Theorem sylan2i

Step	Hyp	Ref	Expression
1		sylan2i.1	. . 3 |- (ph -> th)
2	1	a1i 10	. 2 |- (ps -> (ph -> th))
3		sylan2i.2	. 2 |- (ps -> ((ch /\ th) -> ta))
4	2, 3	sylan2d 468	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:  syl2ani  637