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Metamath Proof Explorer

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

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