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Metamath Proof Explorer

Theorem alimdv

Description: Deduction form of Theorem 19.20 of Margaris p. 90, see alim . See alimdh and alimd for versions without a distinct variable condition. (Contributed by NM, 3-Apr-1994)

		Ref	Expression
	Hypothesis	alimdv.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	Assertion	alimdv	⊢ ( 𝜑 → ( ∀ 𝑥 𝜓 → ∀ 𝑥 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		alimdv.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		ax-5	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
3	2 1	alimdh	⊢ ( 𝜑 → ( ∀ 𝑥 𝜓 → ∀ 𝑥 𝜒 ) )