Theorem dmeqi

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

	Ref	Expression
Hypothesis	dmeqi.1	$$⊢A=B$$
Assertion	dmeqi	$$⊢\mathrm{dom}A=\mathrm{dom}B$$

Proof

Step	Hyp	Ref	Expression
1		dmeqi.1	$$⊢A=B$$
2		dmeq	$$⊢A=B\to \mathrm{dom}A=\mathrm{dom}B$$
3	1 2	ax-mp	$$⊢\mathrm{dom}A=\mathrm{dom}B$$