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Theorem lppotoslem 26246
 Description: To show that a point doesn't belong to a line . (For my private use only. Don't use.) (Contributed by FL, 14-Jul-2016.)
Hypotheses
Ref Expression
lppotoslem.6
lppotoslem.8
lppotoslem.9
Assertion
Ref Expression
lppotoslem

Proof of Theorem lppotoslem
StepHypRef Expression
1 lppotoslem.8 . . 3
2 elin 3371 . . . . . 6
3 lppotoslem.6 . . . . . . . . 9
43eleq2d 2363 . . . . . . . 8
5 elsni 3677 . . . . . . . . 9
6 lppotoslem.9 . . . . . . . . . . . 12
7 df-ne 2461 . . . . . . . . . . . . 13
8 pm2.21 100 . . . . . . . . . . . . 13
97, 8sylbi 187 . . . . . . . . . . . 12
106, 9syl 15 . . . . . . . . . . 11
1110com12 27 . . . . . . . . . 10
1211eqcoms 2299 . . . . . . . . 9
135, 12syl 15 . . . . . . . 8
144, 13syl6bi 219 . . . . . . 7
1514pm2.43b 46 . . . . . 6
162, 15sylbir 204 . . . . 5
1716ex 423 . . . 4
1817com23 72 . . 3
191, 18mpcom 32 . 2
2019pm2.01d 161 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 358   wceq 1632   wcel 1696   wne 2459   cin 3164  csn 3653 This theorem is referenced by:  lppotos  26247 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-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-v 2803  df-in 3172  df-sn 3659
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