Theorem sylbb 123

Description: A mixed syllogism inference from two biconditionals. (Contributed by BJ, 30-Mar-2019.)

Hypotheses

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

Assertion

Ref	Expression
sylbb	|- ( ph -> ch )

Proof of Theorem sylbb

Step	Hyp	Ref	Expression
1		sylbb.1	. 2 |- ( ph <-> ps )
2		sylbb.2	. . 3 |- ( ps <-> ch )
3	2	biimpi 120	. 2 |- ( ps -> ch )
4	1, 3	sylbi 121	1 |- ( ph -> 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

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  ctinfom  12421