Theorem syl5rbb 191

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

Hypotheses

Ref	Expression
syl5rbb.1	|- ( ph <-> ps )
syl5rbb.2	|- ( ch -> ( ps <-> th ) )

Assertion

Ref	Expression
syl5rbb	|- ( ch -> ( th <-> ph ) )

Proof of Theorem syl5rbb

Step	Hyp	Ref	Expression
1		syl5rbb.1	. . 3 |- ( ph <-> ps )
2		syl5rbb.2	. . 3 |- ( ch -> ( ps <-> th ) )
3	1, 2	syl5bb 190	. 2 |- ( ch -> ( ph <-> th ) )
4	3	bicomd 139	1 |- ( ch -> ( th <-> ph ) )

Syntax hints:   -> wi 4   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  syl5rbbr  193  pm5.17dc  844  dn1dc  902  csbabg  2972  uniiunlem  3091  inimasn  4791  cnvpom  4910  fnresdisj  5060  f1oiso  5516  reldm  5863  1idprl  6894  1idpru  6895  nndiv  8198  fzn  9189  fz1sbc  9241  bj-indeq  10991