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	$$⊢\forall x\phi$$
Assertion	bj-ala1i	$$⊢\forall x\left(\psi \to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bj-ala1i.1	$$⊢\forall x\phi$$
2		ala1	$$⊢\forall x\phi \to \forall x\left(\psi \to \phi \right)$$
3	1 2	ax-mp	$$⊢\forall x\left(\psi \to \phi \right)$$