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Theorem elALT 4399
 Description: Every set is an element of some other set. This has a shorter proof than el 4373 but uses more axioms. (Contributed by NM, 4-Jan-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
elALT
Distinct variable group:   ,

Proof of Theorem elALT
StepHypRef Expression
1 vex 2951 . . 3
21snid 3833 . 2
3 snex 4397 . . 3
4 eleq2 2496 . . 3
53, 4spcev 3035 . 2
62, 5ax-mp 8 1
 Colors of variables: wff set class Syntax hints:  wex 1550   wcel 1725  csn 3806 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-v 2950  df-dif 3315  df-un 3317  df-nul 3621  df-sn 3812  df-pr 3813
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