Theorem syl2anbr 466

Description: A double syllogism inference. (Contributed by NM, 29-Jul-1999.)

Hypotheses

Ref	Expression
syl2anbr.1	|- (ps <-> ph)
syl2anbr.2	|- (ch <-> ta)
syl2anbr.3	|- ((ps /\ ch) -> th)

Assertion

Ref	Expression
syl2anbr	|- ((ph /\ ta) -> th)

Proof of Theorem syl2anbr

Step	Hyp	Ref	Expression
1		syl2anbr.2	. 2 |- (ch <-> ta)
2		syl2anbr.1	. . 3 |- (ps <-> ph)
3		syl2anbr.3	. . 3 |- ((ps /\ ch) -> th)
4	2, 3	sylanbr 459	. 2 |- ((ph /\ ch) -> th)
5	1, 4	sylan2br 462	1 |- ((ph /\ ta) -> 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:  sylancbr  647  ov3  5600