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Theorem mapdordlem1bN 32447
Description: Lemma for mapdord 32450. (Contributed by NM, 27-Jan-2015.) (New usage is discouraged.)
Hypothesis
Ref Expression
mapdordlem1b.c  |-  C  =  { g  e.  F  |  ( O `  ( O `  ( L `
 g ) ) )  =  ( L `
 g ) }
Assertion
Ref Expression
mapdordlem1bN  |-  ( J  e.  C  <->  ( J  e.  F  /\  ( O `  ( O `  ( L `  J
) ) )  =  ( L `  J
) ) )
Distinct variable groups:    g, F    g, J    g, L    g, O
Allowed substitution hint:    C( g)

Proof of Theorem mapdordlem1bN
StepHypRef Expression
1 mapdordlem1b.c . 2  |-  C  =  { g  e.  F  |  ( O `  ( O `  ( L `
 g ) ) )  =  ( L `
 g ) }
21lcfl1lem 32303 1  |-  ( J  e.  C  <->  ( J  e.  F  /\  ( O `  ( O `  ( L `  J
) ) )  =  ( L `  J
) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358    = wceq 1632    e. wcel 1696   {crab 2560   ` cfv 5271
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
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-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-rab 2565  df-v 2803  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
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