Theorem spimv

Description: A version of spim with a distinct variable requirement instead of a bound-variable hypothesis. See spimfv and spimvw for versions requiring fewer axioms. (Contributed by NM, 31-Jul-1993) Usage of this theorem is discouraged because it depends on ax-13 . Use spimvw instead. (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		spimv.1	$$⊢x=y\to \left(\phi \to \psi \right)$$
2		nfv	$$⊢Ⅎx\psi$$
3	2 1	spim	$$⊢\forall x\phi \to \psi$$