Theorem sylani 686

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 11	. 2 |- ( ps -> ( ph -> ch ) )
3		sylani.2	. 2 |- ( ps -> ( ( ch /\ th ) -> ta ) )
4	2, 3	syland 498	1 |- ( ps -> ( ( ph /\ th ) -> ta ) )

Syntax hints:   -> wi 4   /\ wa 384

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 197  df-an 386

This theorem is referenced by:  syl2ani  688  inf3lem2  8526  zorn2lem5  9322  uzwo  11751  supxrun  12146  lcmdvds  15321  cramer0  20496  csmdsymi  29193  matunitlindflem2  33406  pmapjoin  35138