Theorem symdifeq2

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

	Ref	Expression
Assertion	symdifeq2	⊢ ( 𝐴 = 𝐵 → ( 𝐶 △ 𝐴 ) = ( 𝐶 △ 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		symdifeq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 △ 𝐶 ) = ( 𝐵 △ 𝐶 ) )
2		symdifcom	⊢ ( 𝐶 △ 𝐴 ) = ( 𝐴 △ 𝐶 )
3		symdifcom	⊢ ( 𝐶 △ 𝐵 ) = ( 𝐵 △ 𝐶 )
4	1 2 3	3eqtr4g	⊢ ( 𝐴 = 𝐵 → ( 𝐶 △ 𝐴 ) = ( 𝐶 △ 𝐵 ) )