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Theorem bnj1071 29420
Description: Technical lemma for bnj69 29453. 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 29211 . 2  |-  ( n  e.  D  ->  n  e.  om )
3 nnord 4856 . 2  |-  ( n  e.  om  ->  Ord  n )
4 ordfr 4599 . 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 1653    e. wcel 1726    \ cdif 3319   (/)c0 3630   {csn 3816    _E cep 4495    Fr wfr 4541   Ord word 4583   omcom 4848
This theorem is referenced by:  bnj1030  29430  bnj1133  29432
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406  ax-un 4704
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-pss 3338  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-tp 3824  df-op 3825  df-uni 4018  df-br 4216  df-opab 4270  df-tr 4306  df-eprel 4497  df-po 4506  df-so 4507  df-fr 4544  df-we 4546  df-ord 4587  df-on 4588  df-lim 4589  df-suc 4590  df-om 4849
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