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Theorem djueq1 9320
 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 2798 . 2 𝐶 = 𝐶
2 djueq12 9319 . 2 ((𝐴 = 𝐵𝐶 = 𝐶) → (𝐴𝐶) = (𝐵𝐶))
31, 2mpan2 690 1 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1538   ⊔ cdju 9313 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-12 2175  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-un 3886  df-opab 5093  df-xp 5525  df-dju 9316 This theorem is referenced by:  djulepw  9605
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