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Axiom ax-c7 2194
Description: Axiom of Quantified Negation. This axiom is used to manipulate negated quantifiers. Equivalent to axiom scheme C7' in [Megill] p. 448 (p. 16 of the preprint). An alternate axiomatization could use axc5c711 2226 in place of ax-c5 2192, ax-c7 2194, and ax-11 1782.

This axiom is obsolete and should no longer be used. It is proved above as theorem axc7 1798. (Contributed by NM, 10-Jan-1993.) (New usage is discouraged.)

Assertion
Ref Expression
ax-c7  |-  ( -. 
A. x  -.  A. x ph  ->  ph )

Detailed syntax breakdown of Axiom ax-c7
StepHypRef Expression
1 wph . . . . . 6  wff  ph
2 vx . . . . . 6  setvar  x
31, 2wal 1368 . . . . 5  wff  A. x ph
43wn 3 . . . 4  wff  -.  A. x ph
54, 2wal 1368 . . 3  wff  A. x  -.  A. x ph
65wn 3 . 2  wff  -.  A. x  -.  A. x ph
76, 1wi 4 1  wff  ( -. 
A. x  -.  A. x ph  ->  ph )
Colors of variables: wff setvar class
This axiom is referenced by:  ax10  2204  ax6fromc10  2205  equid1  2215  axc5c7  2219  axc711  2222  axc5c711  2226  equid1ALT  2233
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