Theorem ax6 711

Description: Axiom C5-2 of [Monk2] p. 113, which we prove from our ax-6 675 (and others). Conversely, ax-6 675 follows from this using ax-4 673 and propositional calculus, showing that they are interchangeable.

Assertion

Ref	Expression
ax6	⊢ (¬ ∀xφ → ∀x ¬ ∀xφ)

Proof of Theorem ax6

Step	Hyp	Ref	Expression
1		hbn1 708	1 ⊢ (¬ ∀xφ → ∀x ¬ ∀xφ)

Syntax hints:  ¬ wn 1   → wi 2  ∀wal 672

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677

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