Theorem raleqOLD

Description: Obsolete version of raleq as of 5-May-2023. Equality theorem for restricted universal quantifier. (Contributed by NM, 16-Nov-1995) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Assertion	raleqOLD	$$⊢A=B\to \left(\forall x\in A\phi \leftrightarrow \forall x\in B\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nfcv	$$⊢\underset{\_}{Ⅎ}xA$$
2		nfcv	$$⊢\underset{\_}{Ⅎ}xB$$
3	1 2	raleqf	$$⊢A=B\to \left(\forall x\in A\phi \leftrightarrow \forall x\in B\phi \right)$$