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Theorem equncom 3168
 Description: If a class equals the union of two other classes, then it equals the union of those two classes commuted. (Contributed by Alan Sare, 18-Feb-2012.)
Assertion
Ref Expression
equncom (𝐴 = (𝐵𝐶) ↔ 𝐴 = (𝐶𝐵))

Proof of Theorem equncom
StepHypRef Expression
1 uncom 3167 . 2 (𝐵𝐶) = (𝐶𝐵)
21eqeq2i 2110 1 (𝐴 = (𝐵𝐶) ↔ 𝐴 = (𝐶𝐵))
 Colors of variables: wff set class Syntax hints:   ↔ wb 104   = wceq 1299   ∪ cun 3019 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082 This theorem depends on definitions:  df-bi 116  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-v 2643  df-un 3025 This theorem is referenced by:  equncomi  3169
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