Mathbox for Frédéric Liné < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  isconcl2b Unicode version

Theorem isconcl2b 26201
 Description: The predicate "are concurrent lines". (For my private use only. Don't use.) (Contributed by FL, 25-Feb-2016.)
Hypothesis
Ref Expression
isconclb Ig
Assertion
Ref Expression
isconcl2b con PLines

Proof of Theorem isconcl2b
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 isconclb . . . 4 Ig
21isconcl1b 26200 . . 3 con PLines
32eleq2d 2363 . 2 con PLines
4 inteq 3881 . . . 4
54neeq1d 2472 . . 3
65elrab 2936 . 2 PLines PLines
73, 6syl6bb 252 1 con PLines
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358   wceq 1632   wcel 1696   wne 2459  crab 2560  c0 3468  cpw 3638  cint 3878  cfv 5271  PLinescplines 26161  Igcig 26163  conccon2 26198 This theorem is referenced by:  isconcl3b  26202  isconcl4b  26203 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-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pow 4204  ax-pr 4230 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-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  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-pw 3640  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-int 3879  df-br 4040  df-opab 4094  df-mpt 4095  df-id 4325  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-iota 5235  df-fun 5273  df-fv 5279  df-con2 26199
 Copyright terms: Public domain W3C validator