Theorem bj-xtageq

Description: The products of a given class and the tagging of either of two equal classes are equal. (Contributed by BJ, 6-Apr-2019)

	Ref	Expression
Assertion	bj-xtageq	⊢ ( 𝐴 = 𝐵 → ( 𝐶 × tag 𝐴 ) = ( 𝐶 × tag 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		bj-tageq	⊢ ( 𝐴 = 𝐵 → tag 𝐴 = tag 𝐵 )
2	1	xpeq2d	⊢ ( 𝐴 = 𝐵 → ( 𝐶 × tag 𝐴 ) = ( 𝐶 × tag 𝐵 ) )