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Theorem uneq2i 3071
Description: Inference adding union to the left in a class equality. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
uneq1i.1 A = B
Assertion
Ref Expression
uneq2i (𝐶A) = (𝐶B)

Proof of Theorem uneq2i
StepHypRef Expression
1 uneq1i.1 . 2 A = B
2 uneq2 3068 . 2 (A = B → (𝐶A) = (𝐶B))
31, 2ax-mp 7 1 (𝐶A) = (𝐶B)
Colors of variables: wff set class
Syntax hints:   = wceq 1228  cun 2892
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 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-un 2899
This theorem is referenced by:  un4  3080  unundir  3082  difun2  3279  difdifdirss  3284  qdass  3441  qdassr  3442  unisuc  4099  iunsuc  4106  fmptap  5278  fvsnun1  5285  rdgi0g  5886  rdgival  5889  rdg0  5895
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