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Theorem bnj923 29114
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 3311 . 2  |-  ( n  e.  ( om  \  { (/)
} )  ->  n  e.  om )
2 bnj923.1 . 2  |-  D  =  ( om  \  { (/)
} )
31, 2eleq2s 2388 1  |-  ( n  e.  D  ->  n  e.  om )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632    e. wcel 1696    \ cdif 3162   (/)c0 3468   {csn 3653   omcom 4672
This theorem is referenced by:  bnj1098  29131  bnj544  29242  bnj546  29244  bnj594  29260  bnj580  29261  bnj966  29292  bnj967  29293  bnj970  29295  bnj1001  29306  bnj1053  29322  bnj1071  29323  bnj1118  29330  bnj1128  29336  bnj1145  29339
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-dif 3168
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