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Theorem inv1 3599
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 3506 . 2  |-  ( A  i^i  _V )  C_  A
2 ssid 3312 . . 3  |-  A  C_  A
3 ssv 3313 . . 3  |-  A  C_  _V
42, 3ssini 3509 . 2  |-  A  C_  ( A  i^i  _V )
51, 4eqssi 3309 1  |-  ( A  i^i  _V )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1649   _Vcvv 2901    i^i cin 3264
This theorem is referenced by:  undif1  3648  dfif4  3695  rint0  4034  iinrab2  4097  riin0  4107  xpriindi  4953  xpssres  5122  imainrect  5254  xpima  5255  dmresv  5271  curry1  6379  curry2  6382  fpar  6391  oev2  6705  gsumxp  15479  pjpm  16860  ptbasfi  17536  hashresfn  23996  dmhashres  23997  mbfmcst  24405  0rrv  24490  pol0N  30025
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-v 2903  df-in 3272  df-ss 3279
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