Theorem sylanr2 397

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 334	. 2 |- ( ( ch /\ ph ) -> ( ch /\ th ) )
3		sylanr2.2	. 2 |- ( ( ps /\ ( ch /\ th ) ) -> ta )
4	2, 3	sylan2 280	1 |- ( ( ps /\ ( ch /\ ph ) ) -> ta )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem is referenced by:  adantrrl  470  adantrrr  471  1stconst  5873  2ndconst  5874  ltexprlemopl  6853  ltexprlemopu  6855  mulsub  7572  fzsubel  9154  expsubap  9621