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Theorem djueq1 7032
Description: Equality theorem for disjoint union. (Contributed by Jim Kingdon, 23-Jun-2022.)
Assertion
Ref Expression
djueq1 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))

Proof of Theorem djueq1
StepHypRef Expression
1 eqid 2177 . 2 𝐶 = 𝐶
2 djueq12 7031 . 2 ((𝐴 = 𝐵𝐶 = 𝐶) → (𝐴𝐶) = (𝐵𝐶))
31, 2mpan2 425 1 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1353  cdju 7029
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-un 3133  df-opab 4062  df-xp 4628  df-dju 7030
This theorem is referenced by:  enumct  7107  ctssexmid  7141  ctiunctal  12412  unct  12413  subctctexmid  14373  sbthom  14397
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