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Metamath Proof Explorer

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	$⊢ \forall x φ \to ψ$
	Assertion	axc4i-o	$⊢ \forall x φ \to \forall x ψ$

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