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Theorem inelcm 3276
Description: The intersection of classes with a common member is nonempty. (Contributed by NM, 7-Apr-1994.)
Assertion
Ref Expression
inelcm  C  i^i  C  =/=  (/)

Proof of Theorem inelcm
StepHypRef Expression
1 elin 3120 . 2  i^i  C  C
2 ne0i 3224 . 2  i^i  C  i^i  C  =/=  (/)
31, 2sylbir 125 1  C  i^i  C  =/=  (/)
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wcel 1390    =/= wne 2201    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-ne 2203  df-v 2553  df-dif 2914  df-in 2918  df-nul 3219
This theorem is referenced by:  minel  3277
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