Theorem dfsymdif2

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

	Ref	Expression
Assertion	dfsymdif2	⊢ ( 𝐴 △ 𝐵 ) = { 𝑥 ∣ ( 𝑥 ∈ 𝐴 ⊻ 𝑥 ∈ 𝐵 ) }

Proof

Step	Hyp	Ref	Expression
1		elsymdifxor	⊢ ( 𝑥 ∈ ( 𝐴 △ 𝐵 ) ↔ ( 𝑥 ∈ 𝐴 ⊻ 𝑥 ∈ 𝐵 ) )
2	1	eqabi	⊢ ( 𝐴 △ 𝐵 ) = { 𝑥 ∣ ( 𝑥 ∈ 𝐴 ⊻ 𝑥 ∈ 𝐵 ) }