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Theorem bnj558 29287
 Description: Technical lemma for bnj852 29306. 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
bnj558.3
bnj558.16
bnj558.17
bnj558.18
bnj558.19
bnj558.20
bnj558.21
bnj558.22
bnj558.23
bnj558.24
bnj558.25
bnj558.28
bnj558.29
bnj558.36
Assertion
Ref Expression
bnj558
Distinct variable groups:   ,,,   ,   ,,,   ,,,   ,,   ,
Allowed substitution hints:   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,)   (,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,)   (,,,,,,)

Proof of Theorem bnj558
StepHypRef Expression
1 bnj558.3 . . 3
2 bnj558.16 . . 3
3 bnj558.17 . . 3
4 bnj558.18 . . 3
5 bnj558.19 . . 3
6 bnj558.20 . . 3
7 bnj558.21 . . 3
8 bnj558.22 . . 3
9 bnj558.23 . . 3
10 bnj558.24 . . 3
11 bnj558.25 . . 3
12 bnj558.28 . . 3
13 bnj558.29 . . 3
14 bnj558.36 . . 3
151, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14bnj557 29286 . 2
16 bnj422 29094 . . . . 5
17 bnj253 29083 . . . . 5
1816, 17bitri 249 . . . 4
1918simp1bi 1012 . . 3
205, 6, 9, 10, 9, 10bnj554 29284 . . 3
2119, 20syl 17 . 2
2215, 21mpbid 210 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 367   w3a 974   wceq 1405   wcel 1842  wral 2754   cdif 3411   cun 3412  c0 3738  csn 3972  cop 3978  ciun 4271   csuc 5412   wfn 5564  cfv 5569  com 6683   w-bnj17 29065   c-bnj14 29067   w-bnj15 29071 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-8 1844  ax-9 1846  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-sep 4517  ax-nul 4525  ax-pr 4630  ax-un 6574  ax-reg 8052 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-eu 2242  df-mo 2243  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2759  df-rex 2760  df-rab 2763  df-v 3061  df-sbc 3278  df-dif 3417  df-un 3419  df-in 3421  df-ss 3428  df-nul 3739  df-if 3886  df-sn 3973  df-pr 3975  df-op 3979  df-uni 4192  df-iun 4273  df-br 4396  df-opab 4454  df-eprel 4734  df-id 4738  df-fr 4782  df-xp 4829  df-rel 4830  df-cnv 4831  df-co 4832  df-dm 4833  df-res 4835  df-suc 5416  df-iota 5533  df-fun 5571  df-fn 5572  df-fv 5577  df-bnj17 29066 This theorem is referenced by:  bnj571  29291
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