Theorem rspcevOLD

Description: Obsolete version of rspce as of 12-Dec-2023. Restricted existential specialization, using implicit substitution. (Contributed by NM, 26-May-1998) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	rspcv.1	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	rspcevOLD	$$⊢\left(A\in B\wedge \psi \right)\to \exists x\in B\phi$$

Proof

Step	Hyp	Ref	Expression
1		rspcv.1	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
2		nfv	$$⊢Ⅎx\psi$$
3	2 1	rspce	$$⊢\left(A\in B\wedge \psi \right)\to \exists x\in B\phi$$