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Theorem bnj923 29137
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj923.1  |-  D  =  ( om  \  { (/)
} )
Assertion
Ref Expression
bnj923  |-  ( n  e.  D  ->  n  e.  om )

Proof of Theorem bnj923
StepHypRef Expression
1 eldifi 3469 . 2  |-  ( n  e.  ( om  \  { (/)
} )  ->  n  e.  om )
2 bnj923.1 . 2  |-  D  =  ( om  \  { (/)
} )
31, 2eleq2s 2528 1  |-  ( n  e.  D  ->  n  e.  om )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652    e. wcel 1725    \ cdif 3317   (/)c0 3628   {csn 3814   omcom 4845
This theorem is referenced by:  bnj1098  29154  bnj544  29265  bnj546  29267  bnj594  29283  bnj580  29284  bnj966  29315  bnj967  29316  bnj970  29318  bnj1001  29329  bnj1053  29345  bnj1071  29346  bnj1118  29353  bnj1128  29359  bnj1145  29362
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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-dif 3323
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