Theorem spv

Description: Specialization, using implicit substitution. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker spvv if possible. (Contributed by NM, 30-Aug-1993) (New usage is discouraged.)

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

Proof

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