Theorem syl2anbr 276

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 269	. 2 |- ((ph /\ ch) -> th)
5	1, 4	sylan2br 272	1 |- ((ph /\ ta) -> th)

Syntax hints:   -> wi 4   /\ wa 97   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  sylancbr  396  tz6.12  5144  ltresr  6736  divmuldivap  7470  fnn0ind  8130