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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). An
alternate axiomatization could use ax467 1659 in place of ax-4 1608,
ax-6o 1613,
and ax-7 1592.
This axiom is redundant, as shown by theorem ax6o 1612. |
| Ref | Expression |
|---|---|
| ax-6o |
     
  |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | wph |
. . . . . 6
 | |
| 2 | vx |
. . . . . 6
 | |
| 3 | 1, 2 | wal 1584 |
. . . . 5
|
| 4 | 3 | wn 2 |
. . . 4
|
| 5 | 4, 2 | wal 1584 |
. . 3
|
| 6 | 5 | wn 2 |
. 2
|
| 7 | 6, 1 | wi 3 |
1
|
| Colors of variables: wff set class |
| This axiom is referenced by: ax6 1614 a6e 1625 hbnt 1638 ax46 1653 ax67 1656 ax467 1659 modal-b 1664 equid 1766 hbntg 14513 ax4567 17183 |