Theorem ax6o 981

Description: Show that the original axiom ax-6o 982 can be derived from ax-6 965 and others. See ax6 983 for the rederivation of ax-6 965 from ax-6o 982.

This theorem should not be referenced in any proof. Instead, use ax-6o 982 below so that uses of ax-6o 982 can be more easily identified.

Assertion

Ref	Expression
ax6o	⊢ (¬ ∀x ¬ ∀xφ → φ)

Proof of Theorem ax6o

Step	Hyp	Ref	Expression
1		ax-4 977	. 2 ⊢ (∀xφ → φ)
2		ax-6 965	. 2 ⊢ (¬ ∀xφ → ∀x ¬ ∀xφ)
3	1, 2	nsyl4 120	1 ⊢ (¬ ∀x ¬ ∀xφ → φ)

Syntax hints:  ¬ wn 2   → wi 3  ∀wal 958

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-6 965  ax-4 977

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