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Theorem bnj1071 29064
Description: Technical lemma for bnj69 29097. 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 28855 . 2  |-  ( n  e.  D  ->  n  e.  om )
3 nnord 4820 . 2  |-  ( n  e.  om  ->  Ord  n )
4 ordfr 4564 . 2  |-  ( Ord  n  ->  _E  Fr  n )
52, 3, 43syl 19 1  |-  ( n  e.  D  ->  _E  Fr  n )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649    e. wcel 1721    \ cdif 3285   (/)c0 3596   {csn 3782    _E cep 4460    Fr wfr 4506   Ord word 4548   omcom 4812
This theorem is referenced by:  bnj1030  29074  bnj1133  29076
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-13 1723  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393  ax-sep 4298  ax-nul 4306  ax-pr 4371  ax-un 4668
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2266  df-mo 2267  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-ne 2577  df-ral 2679  df-rex 2680  df-rab 2683  df-v 2926  df-sbc 3130  df-dif 3291  df-un 3293  df-in 3295  df-ss 3302  df-pss 3304  df-nul 3597  df-if 3708  df-sn 3788  df-pr 3789  df-tp 3790  df-op 3791  df-uni 3984  df-br 4181  df-opab 4235  df-tr 4271  df-eprel 4462  df-po 4471  df-so 4472  df-fr 4509  df-we 4511  df-ord 4552  df-on 4553  df-lim 4554  df-suc 4555  df-om 4813
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