Theorem sylanl2 632

Description: A syllogism inference. (Contributed by NM, 1-Jan-2005.)

Hypotheses

Ref	Expression
sylanl2.1	|- (ph -> ch)
sylanl2.2	|- (((ps /\ ch) /\ th) -> ta)

Assertion

Ref	Expression
sylanl2	|- (((ps /\ ph) /\ th) -> ta)

Proof of Theorem sylanl2

Step	Hyp	Ref	Expression
1		sylanl2.1	. . 3 |- (ph -> ch)
2	1	anim2i 552	. 2 |- ((ps /\ ph) -> (ps /\ ch))
3		sylanl2.2	. 2 |- (((ps /\ ch) /\ th) -> ta)
4	2, 3	sylan 457	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:  mpanlr1  667  adantlrl  700  adantlrr  701  ncssfin  6152  spacind  6288