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Theorem mapdordlem1bN 38924
 Description: Lemma for mapdord 38927. (Contributed by NM, 27-Jan-2015.) (New usage is discouraged.)
Hypothesis
Ref Expression
mapdordlem1b.c 𝐶 = {𝑔𝐹 ∣ (𝑂‘(𝑂‘(𝐿𝑔))) = (𝐿𝑔)}
Assertion
Ref Expression
mapdordlem1bN (𝐽𝐶 ↔ (𝐽𝐹 ∧ (𝑂‘(𝑂‘(𝐿𝐽))) = (𝐿𝐽)))
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 = {𝑔𝐹 ∣ (𝑂‘(𝑂‘(𝐿𝑔))) = (𝐿𝑔)}
21lcfl1lem 38780 1 (𝐽𝐶 ↔ (𝐽𝐹 ∧ (𝑂‘(𝑂‘(𝐿𝐽))) = (𝐿𝐽)))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209   ∧ wa 399   = wceq 1538   ∈ wcel 2112  {crab 3113  ‘cfv 6328 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2159  ax-12 2176  ax-ext 2773 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-nfc 2941  df-rab 3118  df-v 3446  df-un 3889  df-in 3891  df-ss 3901  df-sn 4529  df-pr 4531  df-op 4535  df-uni 4804  df-br 5034  df-iota 6287  df-fv 6336 This theorem is referenced by: (None)
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