Theorem syl6rbb 253

Description: A syllogism inference from two biconditionals. (Contributed by NM, 5-Aug-1993.)

Hypotheses

Ref	Expression
syl6rbb.1	|- (ph -> (ps <-> ch))
syl6rbb.2	|- (ch <-> th)

Assertion

Ref	Expression
syl6rbb	|- (ph -> (th <-> ps))

Proof of Theorem syl6rbb

Step	Hyp	Ref	Expression
1		syl6rbb.1	. . 3 |- (ph -> (ps <-> ch))
2		syl6rbb.2	. . 3 |- (ch <-> th)
3	1, 2	syl6bb 252	. 2 |- (ph -> (ps <-> th))
4	3	bicomd 192	1 |- (ph -> (th <-> ps))

Syntax hints:   -> wi 4   <-> wb 176

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  syl6rbbr  255  bibif  335  pm5.61  693  oranabs  829  necon4bid  2583  resopab2  5002  funconstss  5407  scancan  6332