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Axiom ax-6o 1697
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 1752 in place of ax-4 1692, ax-6o 1697, and ax-7 1535.

This axiom is redundant, as shown by theorem ax6o 1696.

Normally, ax6o 1696 should be used rather than ax-6o 1697, except by theorems specifically studying the latter's properties. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.)

Assertion
Ref Expression
ax-6o  |-  ( -. 
A. x  -.  A. x ph  ->  ph )

Detailed syntax breakdown of Axiom ax-6o
StepHypRef Expression
1 wph . . . . . 6  wff  ph
2 vx . . . . . 6  set  x
31, 2wal 1532 . . . . 5  wff  A. x ph
43wn 5 . . . 4  wff  -.  A. x ph
54, 2wal 1532 . . 3  wff  A. x  -.  A. x ph
65wn 5 . 2  wff  -.  A. x  -.  A. x ph
76, 1wi 6 1  wff  ( -. 
A. x  -.  A. x ph  ->  ph )
Colors of variables: wff set class
This axiom is referenced by:  ax6  1698  ax46  1746  ax67  1749  ax467  1752  equidALT  1819  hbntg  23517  ax4567  26954
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