Axiom ax-6 963

Description: Axiom of Quantified Negation. Axiom C5-2 of [Monk2] p. 113.

Assertion

Ref	Expression
ax-6	⊢ (¬ ∀xφ → ∀x ¬ ∀xφ)

Detailed syntax breakdown of Axiom ax-6

Step	Hyp	Ref	Expression
1		wph	. . . 4 wff φ
2		vx	. . . 4 set x
3	1, 2	wal 956	. . 3 wff ∀xφ
4	3	wn 2	. 2 wff ¬ ∀xφ
5	4, 2	wal 956	. 2 wff ∀x ¬ ∀xφ
6	4, 5	wi 3	1 wff (¬ ∀xφ → ∀x ¬ ∀xφ)

This axiom is referenced by:  ax5o 976  ax6o 979

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