Theorem ala1

Description: Add an antecedent in a universally quantified formula. (Contributed by BJ, 6-Oct-2018)

	Ref	Expression
Assertion	ala1	⊢ ( ∀ 𝑥 𝜑 → ∀ 𝑥 ( 𝜓 → 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		ax-1	⊢ ( 𝜑 → ( 𝜓 → 𝜑 ) )
2	1	alimi	⊢ ( ∀ 𝑥 𝜑 → ∀ 𝑥 ( 𝜓 → 𝜑 ) )