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Theorem uneq1d 3096
 Description: Deduction adding union to the right in a class equality. (Contributed by NM, 29-Mar-1998.)
Hypothesis
Ref Expression
uneq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
uneq1d (𝜑 → (𝐴𝐶) = (𝐵𝐶))

Proof of Theorem uneq1d
StepHypRef Expression
1 uneq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 uneq1 3090 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
31, 2syl 14 1 (𝜑 → (𝐴𝐶) = (𝐵𝐶))
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1243   ∪ cun 2915 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922 This theorem is referenced by:  ifeq1  3334  preq1  3447  tpeq1  3456  tpeq2  3457  resasplitss  5069  fmptpr  5355  rdgisucinc  5972  oasuc  6044  omsuc  6051  fzpred  8932  fseq1p1m1  8956  nn0split  8994  fzo0sn0fzo1  9077  fzosplitprm1  9090
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