Theorem sylani 406

Description: A syllogism inference. (Contributed by NM, 2-May-1996.)

Hypotheses

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

Assertion

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

Proof of Theorem sylani

Step	Hyp	Ref	Expression
1		sylani.1	. . 3 |- ( ph -> ch )
2	1	a1i 9	. 2 |- ( ps -> ( ph -> ch ) )
3		sylani.2	. 2 |- ( ps -> ( ( ch /\ th ) -> ta ) )
4	2, 3	syland 293	1 |- ( ps -> ( ( ph /\ th ) -> ta ) )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  syl2ani  408  fiintim  6992  lcmdvds  12247