Users' Mathboxes Mathbox for Norm Megill < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  mapdordlem1bN Structured version   Visualization version   GIF version

Theorem mapdordlem1bN 41617
Description: Lemma for mapdord 41620. (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 41473 1 (𝐽𝐶 ↔ (𝐽𝐹 ∧ (𝑂‘(𝑂‘(𝐿𝐽))) = (𝐿𝐽)))
Colors of variables: wff setvar class
Syntax hints:  wb 206  wa 395   = wceq 1536  wcel 2105  {crab 3432  cfv 6562
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1539  df-fal 1549  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-rab 3433  df-v 3479  df-dif 3965  df-un 3967  df-ss 3979  df-nul 4339  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4912  df-br 5148  df-iota 6515  df-fv 6570
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator