Theorem bj-2alim 31779

Description: Closed form of 2alimi 1731. (Contributed by BJ, 6-May-2019.)

Assertion

Ref	Expression
bj-2alim	⊢ (∀𝑥∀𝑦(𝜑 → 𝜓) → (∀𝑥∀𝑦𝜑 → ∀𝑥∀𝑦𝜓))

Proof of Theorem bj-2alim

Step	Hyp	Ref	Expression
1		alim 1729	. 2 ⊢ (∀𝑦(𝜑 → 𝜓) → (∀𝑦𝜑 → ∀𝑦𝜓))
2	1	al2imi 1733	1 ⊢ (∀𝑥∀𝑦(𝜑 → 𝜓) → (∀𝑥∀𝑦𝜑 → ∀𝑥∀𝑦𝜓))

Syntax hints:   → wi 4  ∀wal 1473

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1713  ax-4 1728

This theorem is referenced by: (None)