Theorem dfsymdif2

Description: Alternate definition of the symmetric difference. (Contributed by BJ, 30-Apr-2020)

	Ref	Expression
Assertion	dfsymdif2	$$⊢\left(A∆B\right)=\left\{x|\left(x\in A⊻x\in B\right)\right\}$$

Proof

Step	Hyp	Ref	Expression
1		elsymdifxor	$$⊢x\in \left(A∆B\right)\leftrightarrow \left(x\in A⊻x\in B\right)$$
2	1	abbi2i	$$⊢\left(A∆B\right)=\left\{x|\left(x\in A⊻x\in B\right)\right\}$$