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Theorem a9e 1817
 Description: At least one individual exists. This is not a theorem of free logic, which is sound in empty domains. For such a logic, we would add this theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10). In the system consisting of ax-5 1533 through ax-14 1626 and ax-17 1628, all axioms other than ax-9 1684 are believed to be theorems of free logic, although the system without ax-9 1684 is probably not complete in free logic. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
a9e

Proof of Theorem a9e
StepHypRef Expression
1 ax-9 1684 . 2
2 df-ex 1538 . 2
31, 2mpbir 202 1
 Colors of variables: wff set class Syntax hints:   wn 5  wal 1532  wex 1537 This theorem is referenced by:  equid1  1820  equs4  1849  equvini  1879  ax11v2  1935  ax11v2-o  1936  pm11.07  2075  ax11eq  2105  ax11el  2106  ax11inda  2113  euequ1  2201  dtrucor2  4103  snnex  4415  relop  4741  dmi  4800  1st2val  5997  2nd2val  5998  axextnd  8093  ax13dfeq  23323  ax10-16  26773  a9e2eq  27016  a9e2nd  27017  relopabVD  27367  a9e2eqVD  27373  a9e2ndVD  27374  a9e2ndALT  27397  bnj1468  27567  bnj1014  27681  a12stdy1  27815 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-9 1684 This theorem depends on definitions:  df-bi 179  df-ex 1538
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