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Theorem fixcnv 32549
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 3417 . . . 4 𝑥 ∈ V
21, 1brcnv 5541 . . 3 (𝑥𝐴𝑥𝑥𝐴𝑥)
31elfix 32544 . . 3 (𝑥 Fix 𝐴𝑥𝐴𝑥)
41elfix 32544 . . 3 (𝑥 Fix 𝐴𝑥𝐴𝑥)
52, 3, 43bitr4ri 296 . 2 (𝑥 Fix 𝐴𝑥 Fix 𝐴)
65eqriv 2822 1 Fix 𝐴 = Fix 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1656  wcel 2164   class class class wbr 4875  ccnv 5345   Fix cfix 32476
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-13 2389  ax-ext 2803  ax-sep 5007  ax-nul 5015  ax-pr 5129
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-3an 1113  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-mo 2605  df-eu 2640  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-ral 3122  df-rex 3123  df-rab 3126  df-v 3416  df-dif 3801  df-un 3803  df-in 3805  df-ss 3812  df-nul 4147  df-if 4309  df-sn 4400  df-pr 4402  df-op 4406  df-br 4876  df-opab 4938  df-id 5252  df-xp 5352  df-rel 5353  df-cnv 5354  df-dm 5356  df-fix 32500
This theorem is referenced by: (None)
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