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Theorem isig12 26167
 Description: A line is a set of points. (For my private use only. Don't use.) (Contributed by FL, 2-Apr-2016.)
Hypotheses
Ref Expression
isig.1 PPoints
isig.2 PLines
isig12.1 Ig
isig12.2
Assertion
Ref Expression
isig12

Proof of Theorem isig12
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 isig12.2 . 2
2 isig.1 . . 3 PPoints
3 isig.2 . . 3 PLines
4 isig12.1 . . 3 Ig
52, 3, 4isig1a2 26166 . 2
6 sseq1 3212 . . 3
76rspcva 2895 . 2
81, 5, 7syl2anc 642 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1632   wcel 1696  wral 2556   wss 3165  cfv 5271  PPointscpoints 26159  PLinescplines 26161  Igcig 26163 This theorem is referenced by:  lineval12a  26187  iscol3  26197  isconcl5ab  26205  isconcl6a  26206  bsstrs  26249 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  ax-nul 4165 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-eu 2160  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-reu 2563  df-rab 2565  df-v 2803  df-sbc 3005  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-ig2 26164
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