Theorem bj-alrim2

Description: Uncurried (imported) form of bj-alrim . (Contributed by BJ, 2-May-2019)

	Ref	Expression
Assertion	bj-alrim2	⊢ ( ( Ⅎ 𝑥 𝜑 ∧ ∀ 𝑥 ( 𝜑 → 𝜓 ) ) → ( 𝜑 → ∀ 𝑥 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		bj-alrim	⊢ ( Ⅎ 𝑥 𝜑 → ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → ( 𝜑 → ∀ 𝑥 𝜓 ) ) )
2	1	imp	⊢ ( ( Ⅎ 𝑥 𝜑 ∧ ∀ 𝑥 ( 𝜑 → 𝜓 ) ) → ( 𝜑 → ∀ 𝑥 𝜓 ) )