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Theorem 3anbi2i 1179
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 236 . 2  |-  ( ch  <->  ch )
2 3anbi1i.1 . 2  |-  ( ph  <->  ps )
3 biid 236 . 2  |-  ( th  <->  th )
41, 2, 33anbi123i 1176 1  |-  ( ( ch  /\  ph  /\  th )  <->  ( ch  /\  ps  /\  th ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ w3a 965
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 967
This theorem is referenced by:  axgroth4  9004  brfi1uzind  12224  cusgra3v  23377  f13dfv  30152  bnj543  31891  bnj916  31931
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