Theorem sylanbr 345

Description: A syllogism inference.

Hypotheses

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

Assertion

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

Proof of Theorem sylanbr

Step	Hyp	Ref	Expression
1		sylan.1	. 2 |- ((ph /\ ps) -> ch)
2		sylanbr.2	. . 3 |- (ph <-> th)
3	2	biimpr 134	. 2 |- (th -> ph)
4	1, 3	sylan 343	1 |- ((th /\ ps) -> ch)

Syntax hints:   -> wi 2   <-> wb 127   /\ wa 196

This theorem is referenced by:  syl2anbr 351  funfvop 2857  funfv 2862  fvopab2 2878  th3qlem1 3250  axrnegex 4080

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

This theorem depends on definitions:  df-bi 128  df-an 198

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