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Theorem djueq1 6974
 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 2157 . 2 𝐶 = 𝐶
2 djueq12 6973 . 2 ((𝐴 = 𝐵𝐶 = 𝐶) → (𝐴𝐶) = (𝐵𝐶))
31, 2mpan2 422 1 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1335   ⊔ cdju 6971 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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106  df-opab 4026  df-xp 4589  df-dju 6972 This theorem is referenced by:  enumct  7049  ctssexmid  7076  ctiunctal  12142  unct  12143  subctctexmid  13534  sbthom  13560
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