Theorem symdifeq2

Description: Equality theorem for symmetric difference. (Contributed by Scott Fenton, 24-Apr-2012)

	Ref	Expression
Assertion	symdifeq2	$$⊢A=B\to \left(C∆A\right)=\left(C∆B\right)$$

Proof

Step	Hyp	Ref	Expression
1		symdifeq1	$$⊢A=B\to \left(A∆C\right)=\left(B∆C\right)$$
2		symdifcom	$$⊢\left(C∆A\right)=\left(A∆C\right)$$
3		symdifcom	$$⊢\left(C∆B\right)=\left(B∆C\right)$$
4	1 2 3	3eqtr4g	$$⊢A=B\to \left(C∆A\right)=\left(C∆B\right)$$