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Theorem equncomi 3254
Description: Inference form of equncom 3253. (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 3253 . 2 (𝐴 = (𝐵𝐶) ↔ 𝐴 = (𝐶𝐵))
31, 2mpbi 144 1 𝐴 = (𝐶𝐵)
Colors of variables: wff set class
Syntax hints:   = wceq 1335  cun 3100
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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106
This theorem is referenced by:  disjssun  3458  difprsn1  3697  unidmrn  5121  phplem1  6800  djucomen  7154
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