Theorem spcv

Description: Rule of specialization, using implicit substitution. (Contributed by NM, 22-Jun-1994)

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

Proof

Step	Hyp	Ref	Expression
1		spcv.1	$$⊢A\in \mathrm{V}$$
2		spcv.2	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
3	2	spcgv	$$⊢A\in \mathrm{V}\to \left(\forall x\phi \to \psi \right)$$
4	1 3	ax-mp	$$⊢\forall x\phi \to \psi$$