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Theorem isibg2aalem3 26218
 Description: Properties of an incidence-betweenness geometry. (Contributed by FL, 10-Aug-2016.)
Assertion
Ref Expression
isibg2aalem3
Distinct variable groups:   ,   ,   ,   ,   ,   ,

Proof of Theorem isibg2aalem3
StepHypRef Expression
1 neleq2 2551 . . . 4
2 neleq2 2551 . . . 4
3 neleq2 2551 . . . 4
41, 2, 33anbi123d 1252 . . 3
5 ineq2 3377 . . . . . . 7
65eqeq1d 2304 . . . . . 6
7 ineq2 3377 . . . . . . 7
87eqeq1d 2304 . . . . . 6
96, 8anbi12d 691 . . . . 5
10 ineq2 3377 . . . . . 6
1110eqeq1d 2304 . . . . 5
129, 11imbi12d 311 . . . 4
135neeq1d 2472 . . . . . 6
147neeq1d 2472 . . . . . 6
1513, 14anbi12d 691 . . . . 5
1615, 11imbi12d 311 . . . 4
1712, 16anbi12d 691 . . 3
184, 17imbi12d 311 . 2
1918rspcv 2893 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   w3a 934   wceq 1632   wcel 1696   wne 2459   wnel 2460  wral 2556   cin 3164  c0 3468  (class class class)co 5874 This theorem is referenced by:  bsstr  26231  nbssntr  26232 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-nel 2462  df-ral 2561  df-v 2803  df-in 3172
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