Theorem dmeqd

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

	Ref	Expression
Hypothesis	dmeqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	dmeqd	⊢ ( 𝜑 → dom 𝐴 = dom 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		dmeqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		dmeq	⊢ ( 𝐴 = 𝐵 → dom 𝐴 = dom 𝐵 )
3	1 2	syl	⊢ ( 𝜑 → dom 𝐴 = dom 𝐵 )