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Theorem int0 4300
 Description: The intersection of the empty set is the universal class. Exercise 2 of [TakeutiZaring] p. 44. (Contributed by NM, 18-Aug-1993.)
Assertion
Ref Expression
int0

Proof of Theorem int0
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 noel 3788 . . . . . 6
21pm2.21i 131 . . . . 5
32ax-gen 1618 . . . 4
4 equid 1791 . . . 4
53, 42th 239 . . 3
65abbii 2591 . 2
7 df-int 4287 . 2
8 df-v 3111 . 2
96, 7, 83eqtr4i 2496 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  A.wal 1393  =wceq 1395  e.wcel 1818  {cab 2442   cvv 3109   c0 3784  |^|cint 4286 This theorem is referenced by:  unissint  4311  uniintsn  4324  rint0  4327  intex  4608  intnex  4609  oev2  7192  fiint  7817  elfi2  7894  fi0  7900  cardmin2  8400  00lsp  17627  cmpfi  19908  ptbasfi  20082  fbssint  20339  fclscmp  20531  rankeq1o  29828  heibor1lem  30305 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-dif 3478  df-nul 3785  df-int 4287
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