ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  in0 Structured version   Unicode version

Theorem in0 3246
Description: The intersection of a class with the empty set is the empty set. Theorem 16 of [Suppes] p. 26. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
in0  i^i  (/)  (/)

Proof of Theorem in0
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 noel 3222 . . . 4  (/)
21bianfi 853 . . 3  (/)  (/)
32bicomi 123 . 2  (/)  (/)
43ineqri 3124 1  i^i  (/)  (/)
Colors of variables: wff set class
Syntax hints:   wa 97   wceq 1242   wcel 1390    i^i cin 2910   (/)c0 3218
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-dif 2914  df-in 2918  df-nul 3219
This theorem is referenced by:  res0  4559
  Copyright terms: Public domain W3C validator