Theorem indif 2253

Description: Intersection with class difference. Theorem 34 of [Suppes] p. 29.

Assertion

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

Proof of Theorem indif

Step	Hyp	Ref	Expression
1		dfin4 2251	. 2 |- (A i^i (A \ B)) = (A \ (A \ (A \ B)))
2		dfin4 2251	. . 3 |- (A i^i B) = (A \ (A \ B))
3	2	difeq2i 2159	. 2 |- (A \ (A i^i B)) = (A \ (A \ (A \ B)))
4		difin 2248	. 2 |- (A \ (A i^i B)) = (A \ B)
5	1, 3, 4	3eqtr2 1504	1 |- (A i^i (A \ B)) = (A \ B)

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

This theorem is referenced by:  kmlem11 4785

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  df-ss 2056

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