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Theorem cnvcnv2 5487
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 5486 . 2 𝐴 = (𝐴 ∩ (V × V))
2 df-res 5035 . 2 (𝐴 ↾ V) = (𝐴 ∩ (V × V))
31, 2eqtr4i 2629 1 𝐴 = (𝐴 ↾ V)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1474  Vcvv 3167  cin 3533   × cxp 5021  ccnv 5022  cres 5025
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-9 1984  ax-10 2004  ax-11 2019  ax-12 2031  ax-13 2227  ax-ext 2584  ax-sep 4698  ax-nul 4707  ax-pr 4823
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1866  df-eu 2456  df-mo 2457  df-clab 2591  df-cleq 2597  df-clel 2600  df-nfc 2734  df-ral 2895  df-rex 2896  df-rab 2899  df-v 3169  df-dif 3537  df-un 3539  df-in 3541  df-ss 3548  df-nul 3869  df-if 4031  df-sn 4120  df-pr 4122  df-op 4126  df-br 4573  df-opab 4633  df-xp 5029  df-rel 5030  df-cnv 5031  df-res 5035
This theorem is referenced by:  dfrel3  5491  rnresv  5493  rescnvcnv  5496  cocnvcnv1  5544  cocnvcnv2  5545  strfv2d  15674  resnonrel  36715
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