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Theorem uneq1d 3069
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 3063 . 2 (A = B → (A𝐶) = (B𝐶))
31, 2syl 14 1 (φ → (A𝐶) = (B𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1226  cun 2888
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 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-v 2533  df-un 2895
This theorem is referenced by:  ifeq1  3309  preq1  3417  tpeq1  3426  tpeq2  3427  resasplitss  4990  fmptpr  5276  rdgisucinc  5888  oasuc  5955  omsuc  5962
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