Theorem rmoeq1OLD

Description: Obsolete version of rmoeq1 as of 5-May-2023. Equality theorem for restricted at-most-one quantifier. (Contributed by Alexander van der Vekens, 17-Jun-2017) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Assertion	rmoeq1OLD	$$⊢A=B\to \left({\exists }^{*}x\in A\phi \leftrightarrow {\exists }^{*}x\in B\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nfcv	$$⊢\underset{\_}{Ⅎ}xA$$
2		nfcv	$$⊢\underset{\_}{Ⅎ}xB$$
3	1 2	rmoeq1f	$$⊢A=B\to \left({\exists }^{*}x\in A\phi \leftrightarrow {\exists }^{*}x\in B\phi \right)$$