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Theorem tncp 25611
 Description: There exist three non colinear points. (Contributed by FL, 3-Aug-2009.)
Hypothesis
Ref Expression
tncp.1
Assertion
Ref Expression
tncp
Distinct variable groups:   ,,,,   ,,,
Allowed substitution hint:   ()

Proof of Theorem tncp
StepHypRef Expression
1 tncp.1 . . . 4
21isplig 25610 . . 3
32ibi 243 . 2
43simp3d 1013 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 369   w3a 976   wceq 1407   wcel 1844   wne 2600  wral 2756  wrex 2757  wreu 2758  cuni 4193  cplig 25608 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382 This theorem depends on definitions:  df-bi 187  df-an 371  df-3an 978  df-tru 1410  df-ex 1636  df-nf 1640  df-sb 1766  df-eu 2244  df-clab 2390  df-cleq 2396  df-clel 2399  df-nfc 2554  df-ral 2761  df-rex 2762  df-reu 2763  df-v 3063  df-uni 4194  df-plig 25609 This theorem is referenced by:  lpni  25612
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