Theorem ax46 1017

Description: Proof of a single axiom that can replace ax-4 973 and ax-6o 978. See ax46to4 1018 and ax46to6 1019 for the re-derivation of those axioms. (Contributed by Scott Fenton, 12-Sep-2005.)

Assertion

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

Proof of Theorem ax46

Step	Hyp	Ref	Expression
1		ax-6o 978	. 2 ⊢ (¬ ∀x ¬ ∀xφ → φ)
2		ax-4 973	. 2 ⊢ (∀xφ → φ)
3	1, 2	ja 137	1 ⊢ ((∀x ¬ ∀xφ → ∀xφ) → φ)

Syntax hints:  ¬ wn 2   → wi 3  ∀wal 954

This theorem is referenced by:  ax46to4 1018  ax46to6 1019

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 973  ax-6o 978

Copyright terms: Public domain