Theorem vtoclg1f

Description: Version of vtoclgf with one non-freeness hypothesis replaced with a disjoint variable condition, thus avoiding dependency on ax-11 and ax-13 . (Contributed by BJ, 1-May-2019)

	Ref	Expression
Hypotheses	vtoclg1f.nf	$$⊢Ⅎx\psi$$
	vtoclg1f.maj	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
	vtoclg1f.min	$$⊢\phi$$
Assertion	vtoclg1f	$$⊢A\in V\to \psi$$

Proof

Step	Hyp	Ref	Expression
1		vtoclg1f.nf	$$⊢Ⅎx\psi$$
2		vtoclg1f.maj	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
3		vtoclg1f.min	$$⊢\phi$$
4		elisset	$$⊢A\in V\to \exists xx=A$$
5	3 2	mpbii	$$⊢x=A\to \psi$$
6	1 5	exlimi	$$⊢\exists xx=A\to \psi$$
7	4 6	syl	$$⊢A\in V\to \psi$$