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

Theorem el 3922
Description: Every set is an element of some other set. (Contributed by NM, 4-Jan-2002.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
el
Distinct variable group:   ,

Proof of Theorem el
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 zfpow 3919 . 2
2 ax-14 1402 . . . . 5
32alrimiv 1751 . . . 4
4 ax-13 1401 . . . 4
53, 4embantd 50 . . 3
65spimv 1689 . 2
71, 6eximii 1490 1
Colors of variables: wff set class
Syntax hints:   wi 4  wal 1240  wex 1378
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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-13 1401  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-pow 3918
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  dtruarb  3933
  Copyright terms: Public domain W3C validator