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Theorem 3anbi1i 1157
Description: Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)
Hypothesis
Ref Expression
3anbi1i.1 (𝜑𝜓)
Assertion
Ref Expression
3anbi1i ((𝜑𝜒𝜃) ↔ (𝜓𝜒𝜃))

Proof of Theorem 3anbi1i
StepHypRef Expression
1 3anbi1i.1 . 2 (𝜑𝜓)
2 biid 261 . 2 (𝜒𝜒)
3 biid 261 . 2 (𝜃𝜃)
41, 2, 33anbi123i 1155 1 ((𝜑𝜒𝜃) ↔ (𝜓𝜒𝜃))
Colors of variables: wff setvar class
Syntax hints:  wb 206  w3a 1086
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 207  df-an 396  df-3an 1088
This theorem is referenced by:  iinfi  9344  fzolb  13602  brfi1uzind  14449  opfi1uzind  14452  01sqrexlem5  15188  bitsmod  16382  isfunc  17806  txcn  23546  trfil2  23807  isclmp  25030  eulerpartlemn  34365  bnj976  34760  bnj543  34876  bnj594  34895  bnj917  34917  topdifinffinlem  37328  dath  39723  oeord2com  43293  ichexmpl1  47463  grtriproplem  47931  grtrif1o  47934  elfzolborelfzop1  48501  nnolog2flm1  48572  isthincd2  49419
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