Theorem vtocld

Description: Implicit substitution of a class for a setvar variable. (Contributed by Mario Carneiro, 15-Oct-2016)

	Ref	Expression
Hypotheses	vtocld.1	$$⊢\phi \to A\in V$$
	vtocld.2	$$⊢\left(\phi \wedge x=A\right)\to \left(\psi \leftrightarrow \chi \right)$$
	vtocld.3	$$⊢\phi \to \psi$$
Assertion	vtocld	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		vtocld.1	$$⊢\phi \to A\in V$$
2		vtocld.2	$$⊢\left(\phi \wedge x=A\right)\to \left(\psi \leftrightarrow \chi \right)$$
3		vtocld.3	$$⊢\phi \to \psi$$
4		nfv	$$⊢Ⅎx\phi$$
5		nfcvd	$$⊢\phi \to \underset{\_}{Ⅎ}xA$$
6		nfvd	$$⊢\phi \to Ⅎx\chi$$
7	1 2 3 4 5 6	vtocldf	$$⊢\phi \to \chi$$