Theorem sylanbr 459

Description: A syllogism inference. (Contributed by NM, 18-May-1994.)

Hypotheses

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

Assertion

Ref	Expression
sylanbr	|- ((ph /\ ch) -> th)

Proof of Theorem sylanbr

Step	Hyp	Ref	Expression
1		sylanbr.1	. . 3 |- (ps <-> ph)
2	1	biimpri 197	. 2 |- (ph -> ps)
3		sylanbr.2	. 2 |- ((ps /\ ch) -> th)
4	2, 3	sylan 457	1 |- ((ph /\ ch) -> th)

Syntax hints:   -> wi 4   <-> wb 176   /\ wa 358

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 177  df-an 360

This theorem is referenced by:  syl2anbr  466  funfv  5376