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	⊢ ( ∀ 𝑥 𝜑 → 𝜓 )
Assertion	axc4i-o	⊢ ( ∀ 𝑥 𝜑 → ∀ 𝑥 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		axc4i-o.1	⊢ ( ∀ 𝑥 𝜑 → 𝜓 )
2		hba1-o	⊢ ( ∀ 𝑥 𝜑 → ∀ 𝑥 ∀ 𝑥 𝜑 )
3	2 1	alrimih	⊢ ( ∀ 𝑥 𝜑 → ∀ 𝑥 𝜓 )