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Theorem 3anbi2d 1295
Description: Deduction adding conjuncts to an equivalence. (Contributed by NM, 8-Sep-2006.)
Hypothesis
Ref Expression
3anbi1d.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
3anbi2d  |-  ( ph  ->  ( ( th  /\  ps  /\  ta )  <->  ( th  /\  ch  /\  ta )
) )

Proof of Theorem 3anbi2d
StepHypRef Expression
1 biidd 171 . 2  |-  ( ph  ->  ( th  <->  th )
)
2 3anbi1d.1 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
31, 23anbi12d 1291 1  |-  ( ph  ->  ( ( th  /\  ps  /\  ta )  <->  ( th  /\  ch  /\  ta )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104    /\ w3a 962
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 964
This theorem is referenced by:  vtocl3gaf  2755  ordsoexmid  4480  ereq2  6440  genpelxp  7338  seq3f1olemp  10299  qexpclz  10338
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