Theorem sylanr2 403

Description: A syllogism inference. (Contributed by NM, 9-Apr-2005.)

Hypotheses

Ref	Expression
sylanr2.1	|- ( ph -> th )
sylanr2.2	|- ( ( ps /\ ( ch /\ th ) ) -> ta )

Assertion

Ref	Expression
sylanr2	|- ( ( ps /\ ( ch /\ ph ) ) -> ta )

Proof of Theorem sylanr2

Step	Hyp	Ref	Expression
1		sylanr2.1	. . 3 |- ( ph -> th )
2	1	anim2i 340	. 2 |- ( ( ch /\ ph ) -> ( ch /\ th ) )
3		sylanr2.2	. 2 |- ( ( ps /\ ( ch /\ th ) ) -> ta )
4	2, 3	sylan2 284	1 |- ( ( ps /\ ( ch /\ ph ) ) -> ta )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by:  adantrrl  483  adantrrr  484  1stconst  6200  2ndconst  6201  ltexprlemopl  7563  ltexprlemopu  7565  mulsub  8320  fzsubel  10016  expsubap  10524  tgcl  12858