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Theorem equncomi 3273
Description: Inference form of equncom 3272. (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 3272 . 2 (𝐴 = (𝐵𝐶) ↔ 𝐴 = (𝐶𝐵))
31, 2mpbi 144 1 𝐴 = (𝐶𝐵)
Colors of variables: wff set class
Syntax hints:   = wceq 1348  cun 3119
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125
This theorem is referenced by:  disjssun  3478  difprsn1  3719  unidmrn  5143  phplem1  6830  djucomen  7193
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