Definition df-symdif 4177

Description: Define the symmetric difference of two classes. Alternate definitions are dfsymdif2 4185, dfsymdif3 4231 and dfsymdif4 4183. (Contributed by Scott Fenton, 31-Mar-2012.)

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 4176	. 2 class (𝐴 △ 𝐵)
4	1, 2	cdif 3885	. . 3 class (𝐴 ∖ 𝐵)
5	2, 1	cdif 3885	. . 3 class (𝐵 ∖ 𝐴)
6	4, 5	cun 3886	. 2 class ((𝐴 ∖ 𝐵) ∪ (𝐵 ∖ 𝐴))
7	3, 6	wceq 1539	1 wff (𝐴 △ 𝐵) = ((𝐴 ∖ 𝐵) ∪ (𝐵 ∖ 𝐴))

This definition is referenced by:  symdifcom  4178  symdifeq1  4179  nfsymdif  4181  elsymdif  4182  difsssymdif  4187  dfsymdif3  4231  symdif0  5015  symdifv  5016  symdifid  5017