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Theorem 3anbi3i 1157
Description: Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)
Hypothesis
Ref Expression
3anbi1i.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
3anbi3i  |-  ( ( ch  /\  th  /\  ph )  <->  ( ch  /\  th 
/\  ps ) )

Proof of Theorem 3anbi3i
StepHypRef Expression
1 biid 170 . 2  |-  ( ch  <->  ch )
2 biid 170 . 2  |-  ( th  <->  th )
3 3anbi1i.1 . 2  |-  ( ph  <->  ps )
41, 2, 33anbi123i 1153 1  |-  ( ( ch  /\  th  /\  ph )  <->  ( ch  /\  th 
/\  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    /\ w3a 945
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 947
This theorem is referenced by:  dfer2  6396  cbvsum  11080
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