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Axiom ax-6o 2081
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 2112 in place of ax-4 2079, ax-6o 2081, and ax-7 1711.

This axiom is obsolete and should no longer be used. It is proved above as theorem ax6o 1727. (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 1529 . . . . 5  wff  A. x ph
43wn 5 . . . 4  wff  -.  A. x ph
54, 2wal 1529 . . 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  2090  ax9from9o  2091  equid1  2101  ax46  2105  ax67  2108  ax467  2112  equid1ALT  2119
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