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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
StepHypRef Expression
1 syl5rbb.1 . . 3  |-  ( ph  <->  ps )
2 syl5rbb.2 . . 3  |-  ( ch 
->  ( ps  <->  th )
)
31, 2syl5bb 190 . 2  |-  ( ch 
->  ( ph  <->  th )
)
43bicomd 139 1  |-  ( ch 
->  ( th  <->  ph ) )
Colors of variables: wff set class
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
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