Theorem bj-ala1i 37239

Description: Add an antecedent in a universally quantified formula. Inference associated with ala1 1842. (Contributed by BJ, 6-Oct-2018.)

Hypothesis

Ref	Expression
bj-ala1i.1	⊢ ∀𝑥𝜑

Assertion

Ref	Expression
bj-ala1i	⊢ ∀𝑥(𝜓 → 𝜑)

Proof of Theorem bj-ala1i

Step	Hyp	Ref	Expression
1		bj-ala1i.1	. 2 ⊢ ∀𝑥𝜑
2		ala1 1842	. 2 ⊢ (∀𝑥𝜑 → ∀𝑥(𝜓 → 𝜑))
3	1, 2	ax-mp 5	1 ⊢ ∀𝑥(𝜓 → 𝜑)

This proof depends on syntax axioms:   → wi 4  ∀wal 1567

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-gen 1824  ax-4 1838

This theorem is used by: (None)