Theorem sylanl1 382

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 323	. 2 |- ( ( ph /\ ch ) -> ( ps /\ ch ) )
3		sylanl1.2	. 2 |- ( ( ( ps /\ ch ) /\ th ) -> ta )
4	2, 3	sylan 267	1 |- ( ( ( ph /\ ch ) /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem is referenced by:  adantlll  449  adantllr  450  isocnv  5451  nqnq0pi  6536  nqpnq0nq  6551  addnqprl  6627  addnqpru  6628