Theorem bj-2alim 37256

Description: Closed form of 2alimi 1845. (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 1843	. 2 ⊢ (∀𝑦(𝜑 → 𝜓) → (∀𝑦𝜑 → ∀𝑦𝜓))
2	1	al2imi 1848	1 ⊢ (∀𝑥∀𝑦(𝜑 → 𝜓) → (∀𝑥∀𝑦𝜑 → ∀𝑥∀𝑦𝜓))

This proof depends on syntax axioms:   → wi 4  ∀wal 1568

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1828  ax-4 1842

This theorem is used by: (None)