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Axiom ax-c7 34643
Description: Axiom of Quantified Negation. This axiom is used to manipulate negated quantifiers. Equivalent to axiom scheme C7' in [Megill] p. 448 (p. 16 of the preprint). An alternate axiomatization could use axc5c711 34676 in place of ax-c5 34641, ax-c7 34643, and ax-11 2171.

This axiom is obsolete and should no longer be used. It is proved above as theorem axc7 2267. (Contributed by NM, 10-Jan-1993.) (New usage is discouraged.)

Assertion
Ref Expression
ax-c7 (¬ ∀𝑥 ¬ ∀𝑥𝜑𝜑)

Detailed syntax breakdown of Axiom ax-c7
StepHypRef Expression
1 wph . . . . . 6 wff 𝜑
2 vx . . . . . 6 setvar 𝑥
31, 2wal 1618 . . . . 5 wff 𝑥𝜑
43wn 3 . . . 4 wff ¬ ∀𝑥𝜑
54, 2wal 1618 . . 3 wff 𝑥 ¬ ∀𝑥𝜑
65wn 3 . 2 wff ¬ ∀𝑥 ¬ ∀𝑥𝜑
76, 1wi 4 1 wff (¬ ∀𝑥 ¬ ∀𝑥𝜑𝜑)
Colors of variables: wff setvar class
This axiom is referenced by:  ax10fromc7  34653  ax6fromc10  34654  equid1  34657  axc5c7  34669  axc711  34672  axc5c711  34676  equid1ALT  34683
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