Theorem sylani 635

Description: A syllogism inference. (Contributed by NM, 2-May-1996.)

Hypotheses

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

Assertion

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

Proof of Theorem sylani

Step	Hyp	Ref	Expression
1		sylani.1	. . 3 |- (ph -> ch)
2	1	a1i 10	. 2 |- (ps -> (ph -> ch))
3		sylani.2	. 2 |- (ps -> ((ch /\ th) -> ta))
4	2, 3	syland 467	1 |- (ps -> ((ph /\ th) -> 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