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Theorem 3anbi2i 1143
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
3anbi2i  |-  ( ( ch  /\  ph  /\  th )  <->  ( ch  /\  ps  /\  th ) )

Proof of Theorem 3anbi2i
StepHypRef Expression
1 biid 227 . 2  |-  ( ch  <->  ch )
2 3anbi1i.1 . 2  |-  ( ph  <->  ps )
3 biid 227 . 2  |-  ( th  <->  th )
41, 2, 33anbi123i 1140 1  |-  ( ( ch  /\  ph  /\  th )  <->  ( ch  /\  ps  /\  th ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ w3a 934
This theorem is referenced by:  axgroth4  8454  or3dir  23124  bnj543  28925  bnj916  28965
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
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