Theorem 2al2imi 45450

Description: Removes two universal quantifiers from a statement. (Contributed by Andrew Salmon, 24-May-2011.)

Hypothesis

Ref	Expression
2al2imi.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
2al2imi	⊢ (∀𝑥∀𝑦𝜑 → (∀𝑥∀𝑦𝜓 → ∀𝑥∀𝑦𝜒))

Proof of Theorem 2al2imi

Step	Hyp	Ref	Expression
1		2al2imi.1	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
2	1	al2imi 1847	. 2 ⊢ (∀𝑦𝜑 → (∀𝑦𝜓 → ∀𝑦𝜒))
3	2	al2imi 1847	1 ⊢ (∀𝑥∀𝑦𝜑 → (∀𝑥∀𝑦𝜓 → ∀𝑥∀𝑦𝜒))

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

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1827  ax-4 1841

This theorem is used by:  2alim  45454