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Theorem el 4373
 Description: Every set is an element of some other set. See elALT 4399 for a shorter proof using more axioms. (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 4370 . 2
2 ax-14 1729 . . . . 5
32alrimiv 1641 . . . 4
4 ax-13 1727 . . . 4
53, 4embantd 52 . . 3
65spimv 1963 . 2
71, 6eximii 1587 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1549  wex 1550 This theorem is referenced by:  dtru  4382  dvdemo2  4392  axpownd  8468  zfcndinf  8485  domep  25412  distel  25423 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-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-pow 4369 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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