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Theorem intss1 3658
 Description: An element of a class includes the intersection of the class. Exercise 4 of [TakeutiZaring] p. 44 (with correction), generalized to classes. (Contributed by NM, 18-Nov-1995.)
Assertion
Ref Expression
intss1

Proof of Theorem intss1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 vex 2577 . . . 4
21elint 3649 . . 3
3 eleq1 2116 . . . . . 6
4 eleq2 2117 . . . . . 6
53, 4imbi12d 227 . . . . 5
65spcgv 2657 . . . 4
76pm2.43a 49 . . 3
82, 7syl5bi 145 . 2
98ssrdv 2979 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1257   wceq 1259   wcel 1409   wss 2945  cint 3643 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-in 2952  df-ss 2959  df-int 3644 This theorem is referenced by:  intminss  3668  intmin3  3670  intab  3672  int0el  3673  trintssm  3898  inteximm  3931  onnmin  4320  peano5  4349  peano5nnnn  7024  peano5nni  7993  dfuzi  8407  bj-intabssel  10315  bj-intabssel1  10316  peano5setOLD  10452
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