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Theorem djueq1 9762
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 2736 . 2 𝐶 = 𝐶
2 djueq12 9761 . 2 ((𝐴 = 𝐵𝐶 = 𝐶) → (𝐴𝐶) = (𝐵𝐶))
31, 2mpan2 688 1 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1540  cdju 9755
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-v 3443  df-un 3903  df-opab 5155  df-xp 5626  df-dju 9758
This theorem is referenced by:  djulepw  10049
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