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Theorem inv1 3618
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 3525 . 2  |-  ( A  i^i  _V )  C_  A
2 ssid 3331 . . 3  |-  A  C_  A
3 ssv 3332 . . 3  |-  A  C_  _V
42, 3ssini 3528 . 2  |-  A  C_  ( A  i^i  _V )
51, 4eqssi 3328 1  |-  ( A  i^i  _V )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1649   _Vcvv 2920    i^i cin 3283
This theorem is referenced by:  undif1  3667  dfif4  3714  rint0  4054  iinrab2  4118  riin0  4128  xpriindi  4974  xpssres  5143  imainrect  5275  xpima  5276  dmresv  5292  curry1  6401  curry2  6404  fpar  6413  oev2  6730  gsumxp  15509  pjpm  16894  ptbasfi  17570  hashresfn  24113  dmhashres  24114  mbfmcst  24566  0rrv  24666  pol0N  30395
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 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-v 2922  df-in 3291  df-ss 3298
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