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Theorem 0iin 4388
Description: An empty indexed intersection is the universal class. (Contributed by NM, 20-Oct-2005.)
Assertion
Ref Expression
0iin

Proof of Theorem 0iin
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-iin 4333 . 2
2 vex 3112 . . . 4
3 ral0 3934 . . . 4
42, 32th 239 . . 3
54abbi2i 2590 . 2
61, 5eqtr4i 2489 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  e.wcel 1818  {cab 2442  A.wral 2807   cvv 3109   c0 3784  |^|_ciin 4331
This theorem is referenced by:  iinrab2  4393  iinvdif  4402  riin0  4404  iin0  4626  xpriindi  5144  cmpfi  19908  ptbasfi  20082  pol0N  35633
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-ral 2812  df-v 3111  df-dif 3478  df-nul 3785  df-iin 4333
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