Theorem invdif 2249

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 2244	. 2 |- (A i^i (V \ B)) = (A \ (V \ (V \ B)))
2		ddif 2169	. . 3 |- (V \ (V \ B)) = B
3	2	difeq2i 2156	. 2 |- (A \ (V \ (V \ B))) = (A \ B)
4	1, 3	eqtr 1495	1 |- (A i^i (V \ B)) = (A \ B)

Syntax hints:   = wceq 956  Vcvv 1811   \ cdif 2044   i^i cin 2046

This theorem is referenced by:  difundi 2257  difundir 2258  difindi 2259  difindir 2260  difun1 2263  difab 2269  undif1 2340  difdifdir 2346

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-dif 2049  df-in 2051

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