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Theorem bnj1001 29771
 Description: Technical lemma for bnj69 29821. 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.)
Hypotheses
Ref Expression
bnj1001.3
bnj1001.5
bnj1001.6
bnj1001.13
bnj1001.27
Assertion
Ref Expression
bnj1001

Proof of Theorem bnj1001
StepHypRef Expression
1 bnj1001.27 . 2
2 bnj1001.6 . . . . 5
32simplbi 462 . . . 4
43bnj708 29568 . . 3
5 bnj1001.3 . . . . . 6
65bnj1232 29617 . . . . 5
76bnj706 29566 . . . 4
8 bnj1001.13 . . . . 5
98bnj923 29581 . . . 4
107, 9syl 17 . . 3
11 elnn 6714 . . 3
124, 10, 11syl2anc 666 . 2
13 bnj1001.5 . . . . . 6
1413simp3bi 1023 . . . . 5
1514bnj707 29567 . . . 4
16 nnord 6712 . . . . . . 7
17 ordsucelsuc 6661 . . . . . . 7
189, 16, 173syl 18 . . . . . 6
1918biimpa 487 . . . . 5
20 eleq2 2496 . . . . 5
2119, 20anim12i 569 . . . 4
227, 4, 15, 21syl21anc 1264 . . 3
23 bianir 976 . . 3
2422, 23syl 17 . 2
251, 12, 243jca 1186 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371   w3a 983   wceq 1438   wcel 1869   cdif 3434  c0 3762  csn 3997   word 5439   csuc 5442   wfn 5594  cfv 5599  com 6704   w-bnj17 29493 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-8 1871  ax-9 1873  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401  ax-sep 4544  ax-nul 4553  ax-pr 4658  ax-un 6595 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3or 984  df-3an 985  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-eu 2270  df-mo 2271  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-ne 2621  df-ral 2781  df-rex 2782  df-rab 2785  df-v 3084  df-sbc 3301  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-pss 3453  df-nul 3763  df-if 3911  df-sn 3998  df-pr 4000  df-tp 4002  df-op 4004  df-uni 4218  df-br 4422  df-opab 4481  df-tr 4517  df-eprel 4762  df-po 4772  df-so 4773  df-fr 4810  df-we 4812  df-ord 5443  df-on 5444  df-lim 5445  df-suc 5446  df-om 6705  df-bnj17 29494 This theorem is referenced by:  bnj1020  29776
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