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| Description: Axiom of Quantified Negation. This axiom is used to manipulate negated quantifiers. One of the 4 axioms of pure predicate calculus. Equivalent to axiom scheme C7' in [Megill] p. 448 (p. 16 of the preprint). Another equivalent variant ax6-2 1001 appears as Axiom C5-2 of [Monk2] p. 113. An alternate axiomatization could use ax467 997 in place of ax-4 951, ax-6 953, and ax-7 954. |
| Ref | Expression |
|---|---|
| ax-6 |
     
  |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | wph |
. . . . . 6
 | |
| 2 | vx |
. . . . . 6
 | |
| 3 | 1, 2 | wal 950 |
. . . . 5
|
| 4 | 3 | wn 2 |
. . . 4
|
| 5 | 4, 2 | wal 950 |
. . 3
|
| 6 | 5 | wn 2 |
. 2
|
| 7 | 6, 1 | wi 3 |
1
|
| Colors of variables: wff set class |
| This axiom is referenced by: a6e 966 hbnt 978 ax46 991 ax67 994 ax467 997 modal-b 1004 equid 1113 |