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Theorem bnj923 29575
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 3587 . 2  |-  ( n  e.  ( om  \  { (/)
} )  ->  n  e.  om )
2 bnj923.1 . 2  |-  D  =  ( om  \  { (/)
} )
31, 2eleq2s 2530 1  |-  ( n  e.  D  ->  n  e.  om )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1437    e. wcel 1868    \ cdif 3433   (/)c0 3761   {csn 3996   omcom 6703
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-v 3083  df-dif 3439
This theorem is referenced by:  bnj1098  29591  bnj544  29701  bnj546  29703  bnj594  29719  bnj580  29720  bnj966  29751  bnj967  29752  bnj970  29754  bnj1001  29765  bnj1053  29781  bnj1071  29782  bnj1118  29789  bnj1128  29795  bnj1145  29798
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