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Theorem 3anbi1i 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
3anbi1i  |-  ( (
ph  /\  ch  /\  th ) 
<->  ( ps  /\  ch  /\ 
th ) )

Proof of Theorem 3anbi1i
StepHypRef Expression
1 3anbi1i.1 . 2  |-  ( ph  <->  ps )
2 biid 236 . 2  |-  ( ch  <->  ch )
3 biid 236 . 2  |-  ( th  <->  th )
41, 2, 33anbi123i 1177 1  |-  ( (
ph  /\  ch  /\  th ) 
<->  ( ps  /\  ch  /\ 
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:  iinfi  7777  fzolb  11674  sqrlem5  12853  bitsmod  13749  isfunc  14892  istps5OLD  18660  txcn  19330  trfil2  19591  eulerpartlemn  26907  bnj976  32088  bnj543  32203  bnj594  32222  bnj917  32244  dath  33703
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