Theorem vtoclgOLD

Description: Obsolete version of vtoclg as of 26-Jan-2025. (Contributed by NM, 17-Apr-1995) Avoid ax-12 . (Revised by SN, 20-Apr-2024) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	vtoclgOLD.1	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
	vtoclgOLD.2	$$⊢\phi$$
Assertion	vtoclgOLD	$$⊢A\in V\to \psi$$

Proof

Step	Hyp	Ref	Expression
1		vtoclgOLD.1	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
2		vtoclgOLD.2	$$⊢\phi$$
3		elisset	$$⊢A\in V\to \exists xx=A$$
4	2 1	mpbii	$$⊢x=A\to \psi$$
5	4	exlimiv	$$⊢\exists xx=A\to \psi$$
6	3 5	syl	$$⊢A\in V\to \psi$$