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Theorem bnj923 32074
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 3581 . 2  |-  ( n  e.  ( om  \  { (/)
} )  ->  n  e.  om )
2 bnj923.1 . 2  |-  D  =  ( om  \  { (/)
} )
31, 2eleq2s 2560 1  |-  ( n  e.  D  ->  n  e.  om )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1370    e. wcel 1758    \ cdif 3428   (/)c0 3740   {csn 3980   omcom 6581
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1954  ax-ext 2431
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2602  df-v 3074  df-dif 3434
This theorem is referenced by:  bnj1098  32090  bnj544  32200  bnj546  32202  bnj594  32218  bnj580  32219  bnj966  32250  bnj967  32251  bnj970  32253  bnj1001  32264  bnj1053  32280  bnj1071  32281  bnj1118  32288  bnj1128  32294  bnj1145  32297
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