Theorem sylancbr 474

Description: A syllogism inference combined with contraction.

Hypotheses

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

Assertion

Ref	Expression
sylancbr	|- (th -> ch)

Proof of Theorem sylancbr

Step	Hyp	Ref	Expression
1		sylancbr.1	. . 3 |- ((ph /\ ps) -> ch)
2		sylancbr.2	. . 3 |- (ph <-> th)
3		sylancbr.3	. . 3 |- (ps <-> th)
4	1, 2, 3	syl2anbr 456	. 2 |- ((th /\ th) -> ch)
5	4	anidms 434	1 |- (th -> ch)

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223

This theorem is referenced by:  sucxpdom 4846

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

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