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Theorem bnj923 34246
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 3612 . 2  |-  ( n  e.  ( om  \  { (/)
} )  ->  n  e.  om )
2 bnj923.1 . 2  |-  D  =  ( om  \  { (/)
} )
31, 2eleq2s 2562 1  |-  ( n  e.  D  ->  n  e.  om )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1398    e. wcel 1823    \ cdif 3458   (/)c0 3783   {csn 4016   omcom 6673
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-v 3108  df-dif 3464
This theorem is referenced by:  bnj1098  34262  bnj544  34372  bnj546  34374  bnj594  34390  bnj580  34391  bnj966  34422  bnj967  34423  bnj970  34425  bnj1001  34436  bnj1053  34452  bnj1071  34453  bnj1118  34460  bnj1128  34466  bnj1145  34469
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