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Theorem fixcnv 33255
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 3502 . . . 4 𝑥 ∈ V
21, 1brcnv 5751 . . 3 (𝑥𝐴𝑥𝑥𝐴𝑥)
31elfix 33250 . . 3 (𝑥 Fix 𝐴𝑥𝐴𝑥)
41elfix 33250 . . 3 (𝑥 Fix 𝐴𝑥𝐴𝑥)
52, 3, 43bitr4ri 305 . 2 (𝑥 Fix 𝐴𝑥 Fix 𝐴)
65eqriv 2822 1 Fix 𝐴 = Fix 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1530  wcel 2107   class class class wbr 5062  ccnv 5552   Fix cfix 33182
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2797  ax-sep 5199  ax-nul 5206  ax-pr 5325
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-3an 1083  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-mo 2619  df-eu 2651  df-clab 2804  df-cleq 2818  df-clel 2897  df-nfc 2967  df-ral 3147  df-rex 3148  df-rab 3151  df-v 3501  df-dif 3942  df-un 3944  df-in 3946  df-ss 3955  df-nul 4295  df-if 4470  df-sn 4564  df-pr 4566  df-op 4570  df-br 5063  df-opab 5125  df-id 5458  df-xp 5559  df-rel 5560  df-cnv 5561  df-dm 5563  df-fix 33206
This theorem is referenced by: (None)
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