Theorem dmeqi

Description: Equality inference for domain. (Contributed by NM, 4-Mar-2004)

	Ref	Expression
Hypothesis	dmeqi.1	⊢ 𝐴 = 𝐵
Assertion	dmeqi	⊢ dom 𝐴 = dom 𝐵

Proof

Step	Hyp	Ref	Expression
1		dmeqi.1	⊢ 𝐴 = 𝐵
2		dmeq	⊢ ( 𝐴 = 𝐵 → dom 𝐴 = dom 𝐵 )
3	1 2	ax-mp	⊢ dom 𝐴 = dom 𝐵