Theorem vtoclALT

Description: Alternate proof of vtocl . Shorter but requires more axioms. (Contributed by NM, 30-Aug-1993) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	vtoclALT.1	$$⊢A\in \mathrm{V}$$
	vtoclALT.2	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
	vtoclALT.3	$$⊢\phi$$
Assertion	vtoclALT	$$⊢\psi$$

Proof

Step	Hyp	Ref	Expression
1		vtoclALT.1	$$⊢A\in \mathrm{V}$$
2		vtoclALT.2	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
3		vtoclALT.3	$$⊢\phi$$
4		nfv	$$⊢Ⅎx\psi$$
5	4 1 2 3	vtoclf	$$⊢\psi$$