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Theorem bnj1071 28752
Description: Technical lemma for bnj69 28785. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1071.7  |-  D  =  ( om  \  { (/)
} )
Assertion
Ref Expression
bnj1071  |-  ( n  e.  D  ->  _E  Fr  n )

Proof of Theorem bnj1071
StepHypRef Expression
1 bnj1071.7 . . 3  |-  D  =  ( om  \  { (/)
} )
21bnj923 28543 . 2  |-  ( n  e.  D  ->  n  e.  om )
3 nnord 4743 . 2  |-  ( n  e.  om  ->  Ord  n )
4 ordfr 4486 . 2  |-  ( Ord  n  ->  _E  Fr  n )
52, 3, 43syl 18 1  |-  ( n  e.  D  ->  _E  Fr  n )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1642    e. wcel 1710    \ cdif 3225   (/)c0 3531   {csn 3716    _E cep 4382    Fr wfr 4428   Ord word 4470   omcom 4735
This theorem is referenced by:  bnj1030  28762  bnj1133  28764
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-13 1712  ax-14 1714  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339  ax-sep 4220  ax-nul 4228  ax-pr 4293  ax-un 4591
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2213  df-mo 2214  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-ral 2624  df-rex 2625  df-rab 2628  df-v 2866  df-sbc 3068  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-pss 3244  df-nul 3532  df-if 3642  df-sn 3722  df-pr 3723  df-tp 3724  df-op 3725  df-uni 3907  df-br 4103  df-opab 4157  df-tr 4193  df-eprel 4384  df-po 4393  df-so 4394  df-fr 4431  df-we 4433  df-ord 4474  df-on 4475  df-lim 4476  df-suc 4477  df-om 4736
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