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

Theorem inelcm 3423
 Description: The intersection of classes with a common member is nonempty. (Contributed by NM, 7-Apr-1994.)
Assertion
Ref Expression
inelcm

Proof of Theorem inelcm
StepHypRef Expression
1 elin 3259 . 2
2 ne0i 3369 . 2
31, 2sylbir 134 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wcel 1480   wne 2308   cin 3070  c0 3363 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ne 2309  df-v 2688  df-dif 3073  df-in 3077  df-nul 3364 This theorem is referenced by:  minel  3424  disjiun  3924
 Copyright terms: Public domain W3C validator