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Theorem equncomi 3192
Description: Inference form of equncom 3191. (Contributed by Alan Sare, 18-Feb-2012.)
Hypothesis
Ref Expression
equncomi.1 𝐴 = (𝐵𝐶)
Assertion
Ref Expression
equncomi 𝐴 = (𝐶𝐵)

Proof of Theorem equncomi
StepHypRef Expression
1 equncomi.1 . 2 𝐴 = (𝐵𝐶)
2 equncom 3191 . 2 (𝐴 = (𝐵𝐶) ↔ 𝐴 = (𝐶𝐵))
31, 2mpbi 144 1 𝐴 = (𝐶𝐵)
Colors of variables: wff set class
Syntax hints:   = wceq 1316  cun 3039
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-un 3045
This theorem is referenced by:  disjssun  3396  difprsn1  3629  unidmrn  5041  phplem1  6714  djucomen  7040
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