Theorem vtoclg

Description: Implicit substitution of a class expression for a setvar variable. (Contributed by NM, 17-Apr-1995) Avoid ax-12 . (Revised by SN, 20-Apr-2024)

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

Proof

Step	Hyp	Ref	Expression
1		vtoclg.1	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
2		vtoclg.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	$$⊢A\in V\to \psi$$