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Theorem equncom 3082
 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 3081 . 2 (B𝐶) = (𝐶B)
21eqeq2i 2047 1 (A = (B𝐶) ↔ A = (𝐶B))
 Colors of variables: wff set class Syntax hints:   ↔ wb 98   = wceq 1242   ∪ cun 2909 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916 This theorem is referenced by:  equncomi  3083
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