Definition df-in 3214

Description: Define the intersection of two classes. See elin 3220 for membership. (Contributed by SF, 10-Jan-2015.)

Assertion

Ref	Expression
df-in	⊢ (A ∩ B) = ∼ (A ⩃ B)

Detailed syntax breakdown of Definition df-in

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cB	. . 3 class B
3	1, 2	cin 3209	. 2 class (A ∩ B)
4	1, 2	cnin 3205	. . 3 class (A ⩃ B)
5	4	ccompl 3206	. 2 class ∼ (A ⩃ B)
6	3, 5	wceq 1642	1 wff (A ∩ B) = ∼ (A ⩃ B)

This definition is referenced by:  elin  3220  nfin  3231  difeq1  3247  difeq2  3248  dfin5  3546  incompl  4074  inexg  4101