Theorem invdif 2252

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 2247	. 2 |- (A i^i (V \ B)) = (A \ (V \ (V \ B)))
2		ddif 2172	. . 3 |- (V \ (V \ B)) = B
3	2	difeq2i 2159	. 2 |- (A \ (V \ (V \ B))) = (A \ B)
4	1, 3	eqtr 1498	1 |- (A i^i (V \ B)) = (A \ B)

Syntax hints:   = wceq 958  Vcvv 1814   \ cdif 2047   i^i cin 2049

This theorem is referenced by:  difundi 2260  difundir 2261  difindi 2262  difindir 2263  difun1 2266  difab 2272  undif1 2344  difdifdir 2350

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-v 1815  df-dif 2052  df-in 2054

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