Theorem djueq2 6926

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

Step	Hyp	Ref	Expression
1		eqid 2139	. 2 |- C = C
2		djueq12 6924	. 2 |- ( ( C = C /\ A = B ) -> ( C ⊔ A ) = ( C ⊔ B ) )
3	1, 2	mpan 420	1 |- ( A = B -> ( C ⊔ A ) = ( C ⊔ B ) )

Syntax hints:   -> wi 4   = wceq 1331   ⊔ cdju 6922

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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-opab 3990  df-xp 4545  df-dju 6923

This theorem is referenced by: (None)