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Theorem 3anbi1d 1248
Description: Deduction adding conjuncts to an equivalence. (Contributed by NM, 8-Sep-2006.)
Hypothesis
Ref Expression
3anbi1d.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
3anbi1d  |-  ( ph  ->  ( ( ps  /\  th 
/\  ta )  <->  ( ch  /\ 
th  /\  ta )
) )

Proof of Theorem 3anbi1d
StepHypRef Expression
1 3anbi1d.1 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
2 biidd 170 . 2  |-  ( ph  ->  ( th  <->  th )
)
31, 23anbi12d 1245 1  |-  ( ph  ->  ( ( ps  /\  th 
/\  ta )  <->  ( ch  /\ 
th  /\  ta )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103    /\ w3a 920
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  df-3an 922
This theorem is referenced by:  vtocl3gaf  2668  ordsoexmid  4313  genpelxp  6763
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