Definition df-dif 3216

Description: Define the difference of two classes. See eldif 3222 for membership. (Contributed by SF, 10-Jan-2015.)

Assertion

Ref	Expression
df-dif	⊢ (A ∖ B) = (A ∩ ∼ B)

Detailed syntax breakdown of Definition df-dif

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cB	. . 3 class B
3	1, 2	cdif 3207	. 2 class (A ∖ B)
4	2	ccompl 3206	. . 3 class ∼ B
5	1, 4	cin 3209	. 2 class (A ∩ ∼ B)
6	3, 5	wceq 1642	1 wff (A ∖ B) = (A ∩ ∼ B)

This definition is referenced by:  eldif  3222  nfdif  3233  difeq1  3247  difeq2  3248  difsscompl  3550  compldif  4070  inindif  4076  difexg  4103  nnsucelrlem3  4427  ssfin  4471  sbthlem1  6204