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Theorem fixcnv 35909
Description: The fixpoints of a class are the same as those of its converse. (Contributed by Scott Fenton, 16-Apr-2012.)
Assertion
Ref Expression
fixcnv Fix 𝐴 = Fix 𝐴

Proof of Theorem fixcnv
Dummy variable 𝑥 is distinct from all other variables.
StepHypRef Expression
1 vex 3484 . . . 4 𝑥 ∈ V
21, 1brcnv 5893 . . 3 (𝑥𝐴𝑥𝑥𝐴𝑥)
31elfix 35904 . . 3 (𝑥 Fix 𝐴𝑥𝐴𝑥)
41elfix 35904 . . 3 (𝑥 Fix 𝐴𝑥𝐴𝑥)
52, 3, 43bitr4ri 304 . 2 (𝑥 Fix 𝐴𝑥 Fix 𝐴)
65eqriv 2734 1 Fix 𝐴 = Fix 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  wcel 2108   class class class wbr 5143  ccnv 5684   Fix cfix 35836
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pr 5432
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-in 3958  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-br 5144  df-opab 5206  df-id 5578  df-xp 5691  df-rel 5692  df-cnv 5693  df-dm 5695  df-fix 35860
This theorem is referenced by: (None)
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