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Theorem 3anbi3d 1297
Description: Deduction adding conjuncts to an equivalence. (Contributed by NM, 8-Sep-2006.)
Hypothesis
Ref Expression
3anbi1d.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
3anbi3d  |-  ( ph  ->  ( ( th  /\  ta  /\  ps )  <->  ( th  /\  ta  /\  ch )
) )

Proof of Theorem 3anbi3d
StepHypRef Expression
1 biidd 171 . 2  |-  ( ph  ->  ( th  <->  th )
)
2 3anbi1d.1 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
31, 23anbi13d 1293 1  |-  ( ph  ->  ( ( th  /\  ta  /\  ps )  <->  ( th  /\  ta  /\  ch )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104    /\ w3a 963
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 965
This theorem is referenced by:  ceqsex3v  2729  ceqsex4v  2730  ceqsex8v  2732  vtocl3gaf  2756  mob  2867  ordsoexmid  4481  tfr1onlemaccex  6249  tfrcllemaccex  6262  fseq1m1p1  9902  summodc  11180  fsum3  11184  divalglemnn  11642  divalglemeunn  11645  divalglemex  11646  divalglemeuneg  11647
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