Theorem spimvALT

Description: Alternate proof of spimv . Note that it requires only ax-1 through ax-5 together with ax6e . Currently, proofs derive from ax6v , but if ax-6 could be used instead, this proof would reduce axiom usage. (Contributed by NM, 31-Jul-1993) Remove dependency on ax-10 . (Revised by BJ, 29-Nov-2020) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		spimv.1	$$⊢x=y\to \left(\phi \to \psi \right)$$
2		ax6e	$$⊢\exists xx=y$$
3	2 1	eximii	$$⊢\exists x\left(\phi \to \psi \right)$$
4	3	19.36iv	$$⊢\forall x\phi \to \psi$$