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Theorem iuneq2i 3801
Description: Equality inference for indexed union. (Contributed by NM, 22-Oct-2003.)
Hypothesis
Ref Expression
iuneq2i.1 (𝑥𝐴𝐵 = 𝐶)
Assertion
Ref Expression
iuneq2i 𝑥𝐴 𝐵 = 𝑥𝐴 𝐶

Proof of Theorem iuneq2i
StepHypRef Expression
1 iuneq2 3799 . 2 (∀𝑥𝐴 𝐵 = 𝐶 𝑥𝐴 𝐵 = 𝑥𝐴 𝐶)
2 iuneq2i.1 . 2 (𝑥𝐴𝐵 = 𝐶)
31, 2mprg 2466 1 𝑥𝐴 𝐵 = 𝑥𝐴 𝐶
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1316  wcel 1465   ciun 3783
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-ral 2398  df-rex 2399  df-v 2662  df-in 3047  df-ss 3054  df-iun 3785
This theorem is referenced by:  dfiunv2  3819  iunrab  3830  iunid  3838  iunin1  3847  2iunin  3849  resiun1  4808  resiun2  4809  dfimafn2  5439  dfmpt  5565  rdgival  6247  uniqs  6455  txbasval  12363
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