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Theorem lcfl1lem 35130
 Description: Property of a functional with a closed kernel. (Contributed by NM, 28-Dec-2014.)
Hypothesis
Ref Expression
lcfl1.c
Assertion
Ref Expression
lcfl1lem
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem lcfl1lem
StepHypRef Expression
1 fveq2 5879 . . . . 5
21fveq2d 5883 . . . 4
32fveq2d 5883 . . 3
43, 1eqeq12d 2486 . 2
5 lcfl1.c . 2
64, 5elrab2 3186 1
 Colors of variables: wff setvar class Syntax hints:   wb 189   wa 376   wceq 1452   wcel 1904  crab 2760  cfv 5589 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-rex 2762  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-uni 4191  df-br 4396  df-iota 5553  df-fv 5597 This theorem is referenced by:  lcfl1  35131  lcfl8b  35143  lclkrlem1  35145  lclkrlem2  35171  lclkr  35172  lcfls1c  35175  lcfrlem9  35189  mapdvalc  35268  mapdval2N  35269  mapdval4N  35271  mapdordlem1a  35273  mapdordlem1bN  35274  mapdrvallem2  35284
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