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Theorem bnj1018 29333
 Description: Technical lemma for bnj69 29379. 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
bnj1018.1
bnj1018.2
bnj1018.3
bnj1018.4
bnj1018.5
bnj1018.7
bnj1018.8
bnj1018.9
bnj1018.10
bnj1018.11
bnj1018.12
bnj1018.13
bnj1018.14
bnj1018.15
bnj1018.16
bnj1018.26
bnj1018.29
bnj1018.30
Assertion
Ref Expression
bnj1018
Distinct variable groups:   ,,,,,   ,,,   ,,   ,,,,,   ,,,,   ,   ,   ,,   ,   ,
Allowed substitution hints:   (,,,,,)   (,,,,,,)   (,,,,,)   (,,,,,)   (,,,,,,)   (,,,,,)   (,)   (,,,,,,)   (,,,,,,)   (,,,)   (,)   (,,,,)   (,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)

Proof of Theorem bnj1018
StepHypRef Expression
1 df-bnj17 29051 . . 3
2 bnj258 29072 . . . . . . . 8
3 bnj1018.29 . . . . . . . 8
42, 3sylbir 205 . . . . . . 7
54ex 424 . . . . . 6
65eximdv 1632 . . . . 5
7 bnj1018.3 . . . . . 6
8 bnj1018.9 . . . . . 6
9 bnj1018.12 . . . . . 6
10 bnj1018.14 . . . . . 6
11 bnj1018.16 . . . . . 6
127, 8, 9, 10, 11bnj985 29324 . . . . 5
136, 12syl6ibr 219 . . . 4
1413imp 419 . . 3
151, 14sylbi 188 . 2
16 bnj1019 29150 . . 3
17 bnj1018.30 . . . . . 6
1817simp3d 971 . . . . 5
19 bnj1018.26 . . . . . . 7
2019bnj1235 29176 . . . . . 6
21 fndm 5544 . . . . . 6
223, 20, 213syl 19 . . . . 5
2318, 22eleqtrrd 2513 . . . 4
2423exlimiv 1644 . . 3
2516, 24sylbir 205 . 2
26 bnj1018.1 . . 3
27 bnj1018.2 . . 3
28 bnj1018.13 . . 3
2911bnj918 29135 . . 3
30 vex 2959 . . . 4
3130sucex 4791 . . 3
3226, 27, 28, 10, 29, 31bnj1015 29332 . 2
3315, 25, 32syl2anc 643 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936  wex 1550   wceq 1652   wcel 1725  cab 2422  wral 2705  wrex 2706  cvv 2956  wsbc 3161   cdif 3317   cun 3318   wss 3320  c0 3628  csn 3814  cop 3817  ciun 4093   csuc 4583  com 4845   cdm 4878   wfn 5449  cfv 5454   w-bnj17 29050   c-bnj14 29052   w-bnj15 29056   c-bnj18 29058 This theorem is referenced by:  bnj1020  29334 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403  ax-un 4701 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-iun 4095  df-br 4213  df-suc 4587  df-dm 4888  df-iota 5418  df-fn 5457  df-fv 5462  df-bnj17 29051  df-bnj18 29059
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