Definition df-symdif 3217

Description: Define the symmetric difference of two classes. Definition IX.9.10, [Rosser] p. 238. (Contributed by SF, 10-Jan-2015.)

Assertion

Ref	Expression
df-symdif	⊢ (A ⊕ B) = ((A ∖ B) ∪ (B ∖ A))

Detailed syntax breakdown of Definition df-symdif

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cB	. . 3 class B
3	1, 2	csymdif 3210	. 2 class (A ⊕ B)
4	1, 2	cdif 3207	. . 3 class (A ∖ B)
5	2, 1	cdif 3207	. . 3 class (B ∖ A)
6	4, 5	cun 3208	. 2 class ((A ∖ B) ∪ (B ∖ A))
7	3, 6	wceq 1642	1 wff (A ⊕ B) = ((A ∖ B) ∪ (B ∖ A))

This definition is used by:  elsymdif  3224  nfsymdif  3234  symdifeq1  3249  symdifeq2  3250  symdifcom  3543  symdifexg  4104