Theorem syl6rbb 186

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 185	. 2 |- (ph -> (ps <-> th))
4	3	bicomd 129	1 |- (ph -> (th <-> ps))

Syntax hints:   -> wi 4   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  syl6rbbr  188  bibif  613  pm5.61  707  oranabs  727  pm5.7dc  860  nbbndc  1282  resopab2  4598  xpcom  4807  elznn0  8036