Theorem axc4i-o

Description: Inference version of ax-c4 . (Contributed by NM, 3-Jan-1993) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	axc4i-o.1	$$⊢\forall x\phi \to \psi$$
Assertion	axc4i-o	$$⊢\forall x\phi \to \forall x\psi$$

Proof

Step	Hyp	Ref	Expression
1		axc4i-o.1	$$⊢\forall x\phi \to \psi$$
2		hba1-o	$$⊢\forall x\phi \to \forall x\forall x\phi$$
3	2 1	alrimih	$$⊢\forall x\phi \to \forall x\psi$$