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Theorem syl5rbbr 184
Description: A syllogism inference from two biconditionals. (Contributed by NM, 25-Nov-1994.)
Hypotheses
Ref Expression
syl5rbbr.1  |-  ( ps  <->  ph )
syl5rbbr.2  |-  ( ch 
->  ( ps  <->  th )
)
Assertion
Ref Expression
syl5rbbr  |-  ( ch 
->  ( th  <->  ph ) )

Proof of Theorem syl5rbbr
StepHypRef Expression
1 syl5rbbr.1 . . 3  |-  ( ps  <->  ph )
21bicomi 123 . 2  |-  ( ph  <->  ps )
3 syl5rbbr.2 . 2  |-  ( ch 
->  ( ps  <->  th )
)
42, 3syl5rbb 182 1  |-  ( ch 
->  ( th  <->  ph ) )
Colors of variables: wff set class
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:  xordc  1283  sbal2  1898  eqsnm  3526  fnressn  5349  fressnfv  5350  eluniimadm  5404  genpassl  6620  genpassu  6621  1idprl  6686  1idpru  6687  axcaucvglemres  6971  negeq0  7263  muleqadd  7647  crap0  7908  addltmul  8159  fzrev  8944  cjap0  9481  cjne0  9482  caucvgrelemrec  9552  lenegsq  9665  elabgf0  9890
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