Theorem dmeqd

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

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

Proof

Step	Hyp	Ref	Expression
1		dmeqd.1	$$⊢\phi \to A=B$$
2		dmeq	$$⊢A=B\to \mathrm{dom}A=\mathrm{dom}B$$
3	1 2	syl	$$⊢\phi \to \mathrm{dom}A=\mathrm{dom}B$$