Theorem syl6rbb 196

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 195	. 2 |- ( ph -> ( ps <-> th ) )
4	3	bicomd 140	1 |- ( ph -> ( th <-> ps ) )

Syntax hints:   -> wi 4   <-> wb 104

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  syl6rbbr  198  bibif  650  pm5.61  744  oranabs  765  pm5.7dc  901  nbbndc  1331  resopab2  4772  xpcom  4990  f1od2  6014  map1  6583  ac6sfi  6668  elznn0  8819  rexuz3  10477