Theorem rneqd

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

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

Proof

Step	Hyp	Ref	Expression
1		rneqd.1	$$⊢\phi \to A=B$$
2		rneq	$$⊢A=B\to \mathrm{ran}A=\mathrm{ran}B$$
3	1 2	syl	$$⊢\phi \to \mathrm{ran}A=\mathrm{ran}B$$