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Theorem 3anbi2d 1223
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 165 . 2  |-  ( ph  ->  ( th  <->  th )
)
2 3anbi1d.1 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
31, 23anbi12d 1219 1  |-  ( ph  ->  ( ( th  /\  ps  /\  ta )  <->  ( th  /\  ch  /\  ta )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 102    /\ w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  vtocl3gaf  2639  ordsoexmid  4314  ereq2  6145  genpelxp  6667  qexpclz  9441
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