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Theorem bnj999 29770
 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
bnj999.1
bnj999.2
bnj999.3
bnj999.7
bnj999.8
bnj999.9
bnj999.10
bnj999.11
bnj999.12
bnj999.15
bnj999.16
Assertion
Ref Expression
bnj999
Distinct variable groups:   ,,,   ,,   ,,   ,   ,,   ,,   ,,,
Allowed substitution hints:   (,,,,,)   (,,,,,)   (,,,,,)   (,,,)   (,,,,,)   (,,,)   (,,,)   (,,,,)   (,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)

Proof of Theorem bnj999
StepHypRef Expression
1 bnj999.3 . . . . . . 7
2 bnj999.7 . . . . . . 7
3 bnj999.8 . . . . . . 7
4 bnj999.9 . . . . . . 7
5 vex 3085 . . . . . . 7
61, 2, 3, 4, 5bnj919 29580 . . . . . 6
7 bnj999.10 . . . . . 6
8 bnj999.11 . . . . . 6
9 bnj999.12 . . . . . 6
10 bnj999.16 . . . . . . 7
1110bnj918 29579 . . . . . 6
126, 7, 8, 9, 11bnj976 29591 . . . . 5
1312bnj1254 29623 . . . 4
1413anim1i 571 . . 3
15 bnj252 29510 . . 3
16 bnj252 29510 . . 3
1714, 15, 163imtr4i 270 . 2
18 ssiun2 4340 . . . 4
1918bnj708 29568 . . 3
20 3simpa 1003 . . . . . 6
2120ancomd 453 . . . . 5
22 simp3 1008 . . . . 5
23 bnj999.2 . . . . . . . 8
2423, 3, 5bnj539 29704 . . . . . . 7
25 bnj999.15 . . . . . . 7
2624, 8, 25, 10bnj965 29755 . . . . . 6
2726bnj228 29545 . . . . 5
2821, 22, 27sylc 63 . . . 4
2928bnj721 29569 . . 3
3019, 29sseqtr4d 3502 . 2
3117, 30syl 17 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371   w3a 983   wceq 1438   wcel 1869  wral 2776  wsbc 3300   cun 3435   wss 3437  c0 3762  csn 3997  cop 4003  ciun 4297   csuc 5442   wfn 5594  cfv 5599  com 6704   w-bnj17 29493   c-bnj14 29495 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-3an 985  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  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-nul 3763  df-if 3911  df-sn 3998  df-pr 4000  df-op 4004  df-uni 4218  df-iun 4299  df-br 4422  df-opab 4481  df-rel 4858  df-cnv 4859  df-co 4860  df-dm 4861  df-iota 5563  df-fun 5601  df-fn 5602  df-fv 5607  df-bnj17 29494 This theorem is referenced by:  bnj1006  29772
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