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.

Step	Hyp	Ref	Expression
1		noel 3788	. . . . . 6
2	1	pm2.21i 131	. . . . 5
3	2	ax-gen 1618	. . . 4
4		equid 1791	. . . 4
5	3, 4	2th 239	. . 3
6	5	abbii 2591	. 2
7		df-int 4287	. 2
8		df-v 3111	. 2
9	6, 7, 8	3eqtr4i 2496	1

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