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Theorem uneq1i 3087
 Description: Inference adding union to the right in a class equality. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
uneq1i.1 A = B
Assertion
Ref Expression
uneq1i (A𝐶) = (B𝐶)

Proof of Theorem uneq1i
StepHypRef Expression
1 uneq1i.1 . 2 A = B
2 uneq1 3084 . 2 (A = B → (A𝐶) = (B𝐶))
31, 2ax-mp 7 1 (A𝐶) = (B𝐶)
 Colors of variables: wff set class Syntax hints:   = 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:  un12  3095  unundi  3098  tpcoma  3455  qdass  3458  qdassr  3459  tpidm12  3460  resasplitss  5012  fmptpr  5298  df2o3  5953
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