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Theorem bnj999 29329
 Description: Technical lemma for bnj69 29380. 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 2960 . . . . . . 7
61, 2, 3, 4, 5bnj919 29137 . . . . . 6
7 bnj999.10 . . . . . 6
8 bnj999.11 . . . . . 6
9 bnj999.12 . . . . . 6
10 bnj999.16 . . . . . . 7
1110bnj918 29136 . . . . . 6
126, 7, 8, 9, 11bnj976 29149 . . . . 5
1312bnj1254 29182 . . . 4
1413anim1i 553 . . 3
15 bnj252 29068 . . 3
16 bnj252 29068 . . 3
1714, 15, 163imtr4i 259 . 2
18 ssiun2 4135 . . . 4
1918bnj708 29125 . . 3
20 3simpa 955 . . . . . 6
2120ancomd 440 . . . . 5
22 simp3 960 . . . . 5
23 bnj999.2 . . . . . . . 8
2423, 3, 5bnj539 29263 . . . . . . 7
25 bnj999.15 . . . . . . 7
2624, 8, 25, 10bnj965 29314 . . . . . 6
2726bnj228 29103 . . . . 5
2821, 22, 27sylc 59 . . . 4
2928bnj721 29126 . . 3
3019, 29sseqtr4d 3386 . 2
3117, 30syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   w3a 937   wceq 1653   wcel 1726  wral 2706  wsbc 3162   cun 3319   wss 3321  c0 3629  csn 3815  cop 3818  ciun 4094   csuc 4584  com 4846   wfn 5450  cfv 5455   w-bnj17 29051   c-bnj14 29053 This theorem is referenced by:  bnj1006  29331 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404  ax-un 4702 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-sbc 3163  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-uni 4017  df-iun 4096  df-br 4214  df-opab 4268  df-rel 4886  df-cnv 4887  df-co 4888  df-dm 4889  df-iota 5419  df-fun 5457  df-fn 5458  df-fv 5463  df-bnj17 29052
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