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Theorem uneq2 3723
 Description: Equality theorem for the union of two classes. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
uneq2 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))

Proof of Theorem uneq2
StepHypRef Expression
1 uneq1 3722 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
2 uncom 3719 . 2 (𝐶𝐴) = (𝐴𝐶)
3 uncom 3719 . 2 (𝐶𝐵) = (𝐵𝐶)
41, 2, 33eqtr4g 2669 1 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1475   ∪ cun 3538 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545 This theorem is referenced by:  uneq12  3724  uneq2i  3726  uneq2d  3729  uneqin  3837  disjssun  3988  uniprg  4386  unexb  6856  undifixp  7830  unxpdom  8052  ackbij1lem16  8940  fin23lem28  9045  ttukeylem6  9219  lcmfun  15196  ipodrsima  16988  mplsubglem  19255  mretopd  20706  iscldtop  20709  dfcon2  21032  nconsubb  21036  comppfsc  21145  spanun  27788  locfinref  29236  isros  29558  unelros  29561  difelros  29562  rossros  29570  inelcarsg  29700  nofulllem1  31101  rankung  31443  paddval  34102  dochsatshp  35758  nacsfix  36293  eldioph4b  36393  eldioph4i  36394  fiuneneq  36794  isotone1  37366  fiiuncl  38259
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