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Theorem djueq2 6930
Description: Equality theorem for disjoint union. (Contributed by Jim Kingdon, 23-Jun-2022.)
Assertion
Ref Expression
djueq2  |-  ( A  =  B  ->  ( C A )  =  ( C B ) )

Proof of Theorem djueq2
StepHypRef Expression
1 eqid 2140 . 2  |-  C  =  C
2 djueq12 6928 . 2  |-  ( ( C  =  C  /\  A  =  B )  ->  ( C A )  =  ( C B ) )
31, 2mpan 421 1  |-  ( A  =  B  ->  ( C A )  =  ( C B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1332   ⊔ cdju 6926
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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2689  df-un 3076  df-opab 3994  df-xp 4549  df-dju 6927
This theorem is referenced by: (None)
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