Theorem sylanl1 631

Description: A syllogism inference. (Contributed by NM, 10-Mar-2005.)

Hypotheses

Ref	Expression
sylanl1.1	|- (ph -> ps)
sylanl1.2	|- (((ps /\ ch) /\ th) -> ta)

Assertion

Ref	Expression
sylanl1	|- (((ph /\ ch) /\ th) -> ta)

Proof of Theorem sylanl1

Step	Hyp	Ref	Expression
1		sylanl1.1	. . 3 |- (ph -> ps)
2	1	anim1i 551	. 2 |- ((ph /\ ch) -> (ps /\ ch))
3		sylanl1.2	. 2 |- (((ps /\ ch) /\ th) -> ta)
4	2, 3	sylan 457	1 |- (((ph /\ ch) /\ 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:  adantlll  698  adantllr  699  isocnv  5491