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Metamath Proof Explorer

Theorem ralrimiv

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 22-Nov-1994) Reduce dependencies on axioms. (Revised by Wolf Lammen, 4-Dec-2019)

		Ref	Expression
	Hypothesis	ralrimiv.1	⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 → 𝜓 ) )
	Assertion	ralrimiv	⊢ ( 𝜑 → ∀ 𝑥 ∈ 𝐴 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		ralrimiv.1	⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 → 𝜓 ) )
2		ax-5	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
3	2 1	hbralrimi	⊢ ( 𝜑 → ∀ 𝑥 ∈ 𝐴 𝜓 )