Theorem spALT

Description: sp can be proven from the other classic axioms. (Contributed by Rohan Ridenour, 3-Nov-2023) (Proof modification is discouraged.) Use sp instead. (New usage is discouraged.)

	Ref	Expression
Assertion	spALT	$$⊢\forall x\phi \to \phi$$

Proof

Step	Hyp	Ref	Expression
1		ax-1	$$⊢\forall x\phi \to \left(x=y\to \forall x\phi \right)$$
2	1	axc4i	$$⊢\forall x\phi \to \forall x\left(x=y\to \forall x\phi \right)$$
3		axc10	$$⊢\forall x\left(x=y\to \forall x\phi \right)\to \phi$$
4	2 3	syl	$$⊢\forall x\phi \to \phi$$