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Theorem cnvcnv2 4798
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 4797 . 2  |-  `' `' A  =  ( A  i^i  ( _V  X.  _V ) )
2 df-res 4377 . 2  |-  ( A  |`  _V )  =  ( A  i^i  ( _V 
X.  _V ) )
31, 2eqtr4i 2105 1  |-  `' `' A  =  ( A  |` 
_V )
Colors of variables: wff set class
Syntax hints:    = wceq 1285   _Vcvv 2602    i^i cin 2973    X. cxp 4363   `'ccnv 4364    |` cres 4367
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3898  ax-pow 3950  ax-pr 3966
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3386  df-sn 3406  df-pr 3407  df-op 3409  df-br 3788  df-opab 3842  df-xp 4371  df-rel 4372  df-cnv 4373  df-res 4377
This theorem is referenced by:  dfrel3  4802  rnresv  4804  rescnvcnv  4807  cocnvcnv1  4855  cocnvcnv2  4856
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