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Theorem djueq2 9368
 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 2758 . 2 𝐶 = 𝐶
2 djueq12 9366 . 2 ((𝐶 = 𝐶𝐴 = 𝐵) → (𝐶𝐴) = (𝐶𝐵))
31, 2mpan 689 1 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1538   ⊔ cdju 9360 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-ext 2729 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2736  df-cleq 2750  df-clel 2830  df-v 3411  df-un 3863  df-opab 5095  df-xp 5530  df-dju 9363 This theorem is referenced by:  nnadju  9657
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