Theorem difeq2i 1585

Description: Inference adding difference to the left in a class equality.

Hypothesis

Ref	Expression
difeq1i.1	|- A = B

Assertion

Ref	Expression
difeq2i	|- (C \ A) = (C \ B)

Proof of Theorem difeq2i

Step	Hyp	Ref	Expression
1		difeq1i.1	. 2 |- A = B
2		difeq2 1583	. 2 |- (A = B -> (C \ A) = (C \ B))
3	1, 2	ax-mp 6	1 |- (C \ A) = (C \ B)

Syntax hints:   = wceq 1091   \ cdif 1484

This theorem is referenced by:  difeq12i 1586  dfun3 1671  dfin3 1672  dfin4 1673  invdif 1674  indif 1675  difundi 1681  difindi 1683  dif23 1688  symdif1 1689  dif0 1756  undifv 1760  difdifdir 1765  dfsdom2 3362  numthlem 3598

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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