Theorem sylbb1 137

Description: A mixed syllogism inference from two biconditionals. (Contributed by BJ, 21-Apr-2019.)

Hypotheses

Ref	Expression
sylbb1.1	|- ( ph <-> ps )
sylbb1.2	|- ( ph <-> ch )

Assertion

Ref	Expression
sylbb1	|- ( ps -> ch )

Proof of Theorem sylbb1

Step	Hyp	Ref	Expression
1		sylbb1.1	. . 3 |- ( ph <-> ps )
2	1	biimpri 133	. 2 |- ( ps -> ph )
3		sylbb1.2	. 2 |- ( ph <-> ch )
4	2, 3	sylib 122	1 |- ( ps -> ch )

Syntax hints:   -> wi 4   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  ontri2orexmidim  4573  nnwosdc  12042  isstructr  12479