Definition df-nin 3212

Description: Define the anti-intersection of two classes. This operation is used implicitly after Axiom P1 of [Hailperin] p. 6, though there does not seem to be any notation for it in the literature. (Contributed by SF, 10-Jan-2015.)

Assertion

Ref	Expression
df-nin	⊢ (A ⩃ B) = {x ∣ (x ∈ A ⊼ x ∈ B)}

Distinct variable groups:   x,A   x,B

Detailed syntax breakdown of Definition df-nin

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cB	. . 3 class B
3	1, 2	cnin 3205	. 2 class (A ⩃ B)
4		vx	. . . . . 6 setvar x
5	4	cv 1641	. . . . 5 class x
6	5, 1	wcel 1710	. . . 4 wff x ∈ A
7	5, 2	wcel 1710	. . . 4 wff x ∈ B
8	6, 7	wnan 1287	. . 3 wff (x ∈ A ⊼ x ∈ B)
9	8, 4	cab 2339	. 2 class {x ∣ (x ∈ A ⊼ x ∈ B)}
10	3, 9	wceq 1642	1 wff (A ⩃ B) = {x ∣ (x ∈ A ⊼ x ∈ B)}

This definition is referenced by:  elning  3218  nfnin  3229  nineq1  3235