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Theorem lcfl1 32352
 Description: Property of a functional with a closed kernel. (Contributed by NM, 31-Dec-2014.)
Hypotheses
Ref Expression
lcfl1.c
lcfl1.g
Assertion
Ref Expression
lcfl1
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem lcfl1
StepHypRef Expression
1 lcfl1.g . . 3
21biantrurd 496 . 2
3 lcfl1.c . . 3
43lcfl1lem 32351 . 2
52, 4syl6rbbr 257 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653   wcel 1726  crab 2711  cfv 5456 This theorem is referenced by:  lcfl2  32353  lcfl5  32356  lcfl5a  32357  lcfl6  32360  lcfl8  32362  lcfl8a  32363  lclkrlem2  32392 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-iota 5420  df-fv 5464
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