Theorem dp2eq12i

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

	Ref	Expression
Hypotheses	dp2eq1i.1	⊢ 𝐴 = 𝐵
	dp2eq12i.2	⊢ 𝐶 = 𝐷
Assertion	dp2eq12i	⊢ _ 𝐴 𝐶 = _ 𝐵 𝐷

Proof

Step	Hyp	Ref	Expression
1		dp2eq1i.1	⊢ 𝐴 = 𝐵
2		dp2eq12i.2	⊢ 𝐶 = 𝐷
3	1	dp2eq1i	⊢ _ 𝐴 𝐶 = _ 𝐵 𝐶
4	2	dp2eq2i	⊢ _ 𝐵 𝐶 = _ 𝐵 𝐷
5	3 4	eqtri	⊢ _ 𝐴 𝐶 = _ 𝐵 𝐷