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Theorem inv1 3301
Description: The intersection of a class with the universal class is itself. Exercise 4.10(k) of [Mendelson] p. 231. (Contributed by NM, 17-May-1998.)
Assertion
Ref Expression
inv1  |-  ( A  i^i  _V )  =  A

Proof of Theorem inv1
StepHypRef Expression
1 inss1 3204 . 2  |-  ( A  i^i  _V )  C_  A
2 ssid 3029 . . 3  |-  A  C_  A
3 ssv 3030 . . 3  |-  A  C_  _V
42, 3ssini 3207 . 2  |-  A  C_  ( A  i^i  _V )
51, 4eqssi 3026 1  |-  ( A  i^i  _V )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1285   _Vcvv 2612    i^i cin 2983
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-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2614  df-in 2990  df-ss 2997
This theorem is referenced by:  rint0  3701  riin0  3775  xpssres  4704  resdmdfsn  4712  imainrect  4830  xpima2m  4832  dmresv  4843
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