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Theorem uneq2 3251
 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 3250 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
2 uncom 3247 . 2 (𝐶𝐴) = (𝐴𝐶)
3 uncom 3247 . 2 (𝐶𝐵) = (𝐵𝐶)
41, 2, 33eqtr4g 2212 1 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1332   ∪ cun 3096 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-v 2711  df-un 3102 This theorem is referenced by:  uneq12  3252  uneq2i  3254  uneq2d  3257  uneqin  3354  disjssun  3453  uniprg  3783  sucprc  4367  unexb  4396  unfiexmid  6851  unfidisj  6855  hashunlem  10655  bdunexb  13441  bj-unexg  13442
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