MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax-c7 Unicode version

Axiom ax-c7 2216
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 2248 in place of ax-c5 2214, ax-c7 2216, and ax-11 1842.

This axiom is obsolete and should no longer be used. It is proved above as theorem axc7 1861. (Contributed by NM, 10-Jan-1993.) (New usage is discouraged.)

Assertion
Ref Expression
ax-c7

Detailed syntax breakdown of Axiom ax-c7
StepHypRef Expression
1 wph . . . . . 6
2 vx . . . . . 6
31, 2wal 1393 . . . . 5
43wn 3 . . . 4
54, 2wal 1393 . . 3
65wn 3 . 2
76, 1wi 4 1
Colors of variables: wff setvar class
This axiom is referenced by:  ax10  2226  ax6fromc10  2227  equid1  2237  axc5c7  2241  axc711  2244  axc5c711  2248  equid1ALT  2255
  Copyright terms: Public domain W3C validator