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Theorem isconcl1b 26200
 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
isconcl1b con PLines
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem isconcl1b
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 isconclb . 2 Ig
2 fveq2 5541 . . . . 5 PLines PLines
32pweqd 3643 . . . 4 PLines PLines
4 biidd 228 . . . 4
53, 4rabeqbidv 2796 . . 3 PLines PLines
6 df-con2 26199 . . 3 con Ig PLines
7 fvex 5555 . . . . 5 PLines
87pwex 4209 . . . 4 PLines
98rabex 4181 . . 3 PLines
105, 6, 9fvmpt 5618 . 2 Ig con PLines
111, 10syl 15 1 con PLines
 Colors of variables: wff set class Syntax hints:   wi 4   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:  isconcl2b  26201 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-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
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