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Theorem 0iin 4151
 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 4098 . 2
2 vex 2961 . . . 4
3 ral0 3734 . . . 4
42, 32th 232 . . 3
54abbi2i 2549 . 2
61, 5eqtr4i 2461 1
 Colors of variables: wff set class Syntax hints:   wceq 1653   wcel 1726  cab 2424  wral 2707  cvv 2958  c0 3630  ciin 4096 This theorem is referenced by:  iinrab2  4156  riin0  4166  iin0  4375  xpriindi  5013  cmpfi  17473  ptbasfi  17615  pol0N  30768 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-v 2960  df-dif 3325  df-nul 3631  df-iin 4098
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