Theorem spvv

Description: Specialization, using implicit substitution. Version of spv with a disjoint variable condition, which does not require ax-7 , ax-12 , ax-13 . (Contributed by NM, 30-Aug-1993) (Revised by BJ, 31-May-2019)

	Ref	Expression
Hypothesis	spvv.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	spvv	$$⊢\forall x\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		spvv.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
2	1	biimpd	$$⊢x=y\to \left(\phi \to \psi \right)$$
3	2	spimvw	$$⊢\forall x\phi \to \psi$$