Theorem difeq12i 1586

Description: Equality inference for class difference.

Hypotheses

Ref	Expression
difeq1i.1	⊢ A = B
difeq12i.2	⊢ C = D

Assertion

Ref	Expression
difeq12i	⊢ (A ∖ C) = (B ∖ D)

Proof of Theorem difeq12i

Step	Hyp	Ref	Expression
1		difeq1i.1	. . 3 ⊢ A = B
2	1	difeq1i 1584	. 2 ⊢ (A ∖ C) = (B ∖ C)
3		difeq12i.2	. . 3 ⊢ C = D
4	3	difeq2i 1585	. 2 ⊢ (B ∖ C) = (B ∖ D)
5	2, 4	eqtr 1119	1 ⊢ (A ∖ C) = (B ∖ D)

Syntax hints:   = wceq 1091   ∖ cdif 1484

This theorem is referenced by:  difrab 1695

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-dif 1489

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