Theorem djueq2 7107

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 2196	. 2 |- C = C
2		djueq12 7105	. 2 |- ( ( C = C /\ A = B ) -> ( C ⊔ A ) = ( C ⊔ B ) )
3	1, 2	mpan 424	1 |- ( A = B -> ( C ⊔ A ) = ( C ⊔ B ) )

Syntax hints:   -> wi 4   = wceq 1364   ⊔ cdju 7103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-v 2765  df-un 3161  df-opab 4095  df-xp 4669  df-dju 7104

This theorem is referenced by: (None)