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Theorem uneq2d 3091
Description: Deduction adding union to the left in a class equality. (Contributed by NM, 29-Mar-1998.)
Hypothesis
Ref Expression
uneq1d.1 (φA = B)
Assertion
Ref Expression
uneq2d (φ → (𝐶A) = (𝐶B))

Proof of Theorem uneq2d
StepHypRef Expression
1 uneq1d.1 . 2 (φA = B)
2 uneq2 3085 . 2 (A = B → (𝐶A) = (𝐶B))
31, 2syl 14 1 (φ → (𝐶A) = (𝐶B))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242  cun 2909
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916
This theorem is referenced by:  ifeq2  3329  tpeq3  3449  iununir  3729  unisucg  4117  relcoi1  4792  resasplitss  5012  fvun1  5182  fmptapd  5297  fvunsng  5300  rdgeq1  5898  rdgivallem  5908  rdgisuc1  5911  rdg0  5914  oav2  5982  oasuc  5983  omv2  5984  omsuc  5990  fzsuc  8661  fseq1p1m1  8686  fseq1m1p1  8687  fzosplitsnm1  8795  fzosplitsn  8819  fzosplitprm1  8820
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