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Theorem djueq2 7053
Description: Equality theorem for disjoint union. (Contributed by Jim Kingdon, 23-Jun-2022.)
Assertion
Ref Expression
djueq2 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))

Proof of Theorem djueq2
StepHypRef Expression
1 eqid 2187 . 2 𝐶 = 𝐶
2 djueq12 7051 . 2 ((𝐶 = 𝐶𝐴 = 𝐵) → (𝐶𝐴) = (𝐶𝐵))
31, 2mpan 424 1 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1363  cdju 7049
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 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-un 3145  df-opab 4077  df-xp 4644  df-dju 7050
This theorem is referenced by: (None)
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