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Axiom ax-6 1703
Description: Axiom of Quantified Negation. Axiom C5-2 of [Monk2] p. 113. This axiom scheme is logically redundant (see ax6w 1691) but is used as an auxiliary axiom to achieve metalogical completeness. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
ax-6  |-  ( -. 
A. x ph  ->  A. x  -.  A. x ph )

Detailed syntax breakdown of Axiom ax-6
StepHypRef Expression
1 wph . . . 4  wff  ph
2 vx . . . 4  set  x
31, 2wal 1527 . . 3  wff  A. x ph
43wn 3 . 2  wff  -.  A. x ph
54, 2wal 1527 . 2  wff  A. x  -.  A. x ph
64, 5wi 4 1  wff  ( -. 
A. x ph  ->  A. x  -.  A. x ph )
Colors of variables: wff set class
This axiom is referenced by:  hbn1  1704  ax6o  1723  ax4567  27601
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