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Theorem bnj1071 31171
 Description: Technical lemma for bnj69 31204. 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 = (ω ∖ {∅})
Assertion
Ref Expression
bnj1071 (𝑛𝐷 → E Fr 𝑛)

Proof of Theorem bnj1071
StepHypRef Expression
1 bnj1071.7 . . 3 𝐷 = (ω ∖ {∅})
21bnj923 30964 . 2 (𝑛𝐷𝑛 ∈ ω)
3 nnord 7115 . 2 (𝑛 ∈ ω → Ord 𝑛)
4 ordfr 5776 . 2 (Ord 𝑛 → E Fr 𝑛)
52, 3, 43syl 18 1 (𝑛𝐷 → E Fr 𝑛)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1523   ∈ wcel 2030   ∖ cdif 3604  ∅c0 3948  {csn 4210   E cep 5057   Fr wfr 5099  Ord word 5760  ωcom 7107 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-8 2032  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631  ax-sep 4814  ax-nul 4822  ax-pr 4936  ax-un 6991 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3or 1055  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-eu 2502  df-mo 2503  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ne 2824  df-ral 2946  df-rex 2947  df-rab 2950  df-v 3233  df-sbc 3469  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-pss 3623  df-nul 3949  df-if 4120  df-sn 4211  df-pr 4213  df-tp 4215  df-op 4217  df-uni 4469  df-br 4686  df-opab 4746  df-tr 4786  df-eprel 5058  df-po 5064  df-so 5065  df-fr 5102  df-we 5104  df-ord 5764  df-on 5765  df-lim 5766  df-suc 5767  df-om 7108 This theorem is referenced by:  bnj1030  31181  bnj1133  31183
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