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Theorem equncom 3065
 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 3064 . 2 (B𝐶) = (𝐶B)
21eqeq2i 2032 1 (A = (B𝐶) ↔ A = (𝐶B))
 Colors of variables: wff set class Syntax hints:   ↔ wb 98   = wceq 1228   ∪ cun 2892 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004 This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-un 2899 This theorem is referenced by:  equncomi  3066
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