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Theorem cnvcnv2 5698
Description: The double converse of a class equals its restriction to the universe. (Contributed by NM, 8-Oct-2007.)
Assertion
Ref Expression
cnvcnv2 𝐴 = (𝐴 ↾ V)

Proof of Theorem cnvcnv2
StepHypRef Expression
1 cnvcnv 5696 . 2 𝐴 = (𝐴 ∩ (V × V))
2 df-res 5230 . 2 (𝐴 ↾ V) = (𝐴 ∩ (V × V))
31, 2eqtr4i 2749 1 𝐴 = (𝐴 ↾ V)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1596  Vcvv 3304  cin 3679   × cxp 5216  ccnv 5217  cres 5220
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-10 2132  ax-11 2147  ax-12 2160  ax-13 2355  ax-ext 2704  ax-sep 4889  ax-nul 4897  ax-pr 5011
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1599  df-ex 1818  df-nf 1823  df-sb 2011  df-eu 2575  df-mo 2576  df-clab 2711  df-cleq 2717  df-clel 2720  df-nfc 2855  df-ral 3019  df-rab 3023  df-v 3306  df-dif 3683  df-un 3685  df-in 3687  df-ss 3694  df-nul 4024  df-if 4195  df-sn 4286  df-pr 4288  df-op 4292  df-br 4761  df-opab 4821  df-xp 5224  df-rel 5225  df-cnv 5226  df-res 5230
This theorem is referenced by:  dfrel3  5702  rnresv  5704  rescnvcnv  5707  cocnvcnv1  5759  cocnvcnv2  5760  strfv2d  16028  resnonrel  38317
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