Theorem bj-ala1i

Description: Add an antecedent in a universally quantified formula. Inference associated with ala1 . (Contributed by BJ, 6-Oct-2018)

	Ref	Expression
Hypothesis	bj-ala1i.1	⊢ ∀ 𝑥 𝜑
Assertion	bj-ala1i	⊢ ∀ 𝑥 ( 𝜓 → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		bj-ala1i.1	⊢ ∀ 𝑥 𝜑
2		ala1	⊢ ( ∀ 𝑥 𝜑 → ∀ 𝑥 ( 𝜓 → 𝜑 ) )
3	1 2	ax-mp	⊢ ∀ 𝑥 ( 𝜓 → 𝜑 )