Theorem ax46 2162

Description: Proof of a single axiom that can replace ax-4 2135 and ax-6o 2137. See ax46to4 2163 and ax46to6 2164 for the re-derivation of those axioms. (Contributed by Scott Fenton, 12-Sep-2005.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
ax46	⊢ ((∀x ¬ ∀xφ → ∀xφ) → φ)

Proof of Theorem ax46

Step	Hyp	Ref	Expression
1		ax-6o 2137	. 2 ⊢ (¬ ∀x ¬ ∀xφ → φ)
2		ax-4 2135	. 2 ⊢ (∀xφ → φ)
3	1, 2	ja 153	1 ⊢ ((∀x ¬ ∀xφ → ∀xφ) → φ)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-4 2135  ax-6o 2137

This theorem is referenced by:  ax46to4  2163  ax46to6  2164