Theorem xpeq1i

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

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

Proof

Step	Hyp	Ref	Expression
1		xpeq1i.1	⊢ 𝐴 = 𝐵
2		xpeq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 × 𝐶 ) = ( 𝐵 × 𝐶 ) )
3	1 2	ax-mp	⊢ ( 𝐴 × 𝐶 ) = ( 𝐵 × 𝐶 )