Theorem invdif 1674

Description: Intersection with universal complement. Remark in [Stoll] p. 20.

Assertion

Ref	Expression
invdif	|- (A i^i (V \ B)) = (A \ B)

Proof of Theorem invdif

Step	Hyp	Ref	Expression
1		dfin2 1669	. 2 |- (A i^i (V \ B)) = (A \ (V \ (V \ B)))
2		ddif 1597	. . 3 |- (V \ (V \ B)) = B
3	2	difeq2i 1585	. 2 |- (A \ (V \ (V \ B))) = (A \ B)
4	1, 3	eqtr 1119	1 |- (A i^i (V \ B)) = (A \ B)

Syntax hints:   = wceq 1091  Vcvv 1348   \ cdif 1484   i^i cin 1486

This theorem is referenced by:  difundi 1681  difundir 1682  difindi 1683  difindir 1684  difun1 1687  difab 1693  undif1 1761  difdifdir 1765

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-v 1349  df-dif 1489  df-in 1491

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