Theorem dp2eq1i

Description: Equality theorem for the decimal expansion constructor. (Contributed by David A. Wheeler, 15-May-2015)

	Ref	Expression
Hypothesis	dp2eq1i.1	⊢ 𝐴 = 𝐵
Assertion	dp2eq1i	⊢ _ 𝐴 𝐶 = _ 𝐵 𝐶

Proof

Step	Hyp	Ref	Expression
1		dp2eq1i.1	⊢ 𝐴 = 𝐵
2		dp2eq1	⊢ ( 𝐴 = 𝐵 → _ 𝐴 𝐶 = _ 𝐵 𝐶 )
3	1 2	ax-mp	⊢ _ 𝐴 𝐶 = _ 𝐵 𝐶