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Theorem uneq2 3068
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 3067 . 2 (A = B → (A𝐶) = (B𝐶))
2 uncom 3064 . 2 (𝐶A) = (A𝐶)
3 uncom 3064 . 2 (𝐶B) = (B𝐶)
41, 2, 33eqtr4g 2079 1 (A = B → (𝐶A) = (𝐶B))
Colors of variables: wff set class
Syntax hints:  wi 4   = 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:  uneq12  3069  uneq2i  3071  uneq2d  3074  uneqin  3165  disjssun  3262  uniprg  3569  sucprc  4098  unexb  4127  bdunexb  7290  bj-unexg  7291
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