Theorem sylbb2 138

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

Hypotheses

Ref	Expression
sylbb2.1	|- ( ph <-> ps )
sylbb2.2	|- ( ch <-> ps )

Assertion

Ref	Expression
sylbb2	|- ( ph -> ch )

Proof of Theorem sylbb2

Step	Hyp	Ref	Expression
1		sylbb2.1	. 2 |- ( ph <-> ps )
2		sylbb2.2	. . 3 |- ( ch <-> ps )
3	2	biimpri 133	. 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  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  inffiexmid  6908  ssfirab  6935  ctssexmid  7150  pw1nel3  7232  fsumsplitsnun  11429