Theorem hbn1 708

Description: x is not free in ¬ ∀xφ.

Assertion

Ref	Expression
hbn1	⊢ (¬ ∀xφ → ∀x ¬ ∀xφ)

Proof of Theorem hbn1

Step	Hyp	Ref	Expression
1		hba1 698	. 2 ⊢ (∀xφ → ∀x∀xφ)
2	1	hbne 699	1 ⊢ (¬ ∀xφ → ∀x ¬ ∀xφ)

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

This theorem is referenced by:  hbe1 709  ax6 711  eqs1 828  eqs2 829  ax15 1006

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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