Theorem xpeq2i

Description: Equality inference for Cartesian product. (Contributed by NM, 21-Dec-2008)

	Ref	Expression
Hypothesis	xpeq1i.1	⊢ 𝐴 = 𝐵
Assertion	xpeq2i	⊢ ( 𝐶 × 𝐴 ) = ( 𝐶 × 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		xpeq1i.1	⊢ 𝐴 = 𝐵
2		xpeq2	⊢ ( 𝐴 = 𝐵 → ( 𝐶 × 𝐴 ) = ( 𝐶 × 𝐵 ) )
3	1 2	ax-mp	⊢ ( 𝐶 × 𝐴 ) = ( 𝐶 × 𝐵 )