Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj557 Structured version   Unicode version

Theorem bnj557 34081
 Description: Technical lemma for bnj852 34101. 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
bnj557.3
bnj557.16
bnj557.17
bnj557.18
bnj557.19
bnj557.20
bnj557.21
bnj557.22
bnj557.23
bnj557.24
bnj557.25
bnj557.28
bnj557.29
bnj557.36
Assertion
Ref Expression
bnj557
Distinct variable groups:   ,,,   ,   ,,,   ,,,   ,,   ,
Allowed substitution hints:   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,)   (,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,)   (,,,,,,)

Proof of Theorem bnj557
StepHypRef Expression
1 3an4anass 1219 . . . . 5
2 bnj557.18 . . . . . . . 8
3 bnj557.19 . . . . . . . 8
42, 3bnj556 34080 . . . . . . 7
543anim3i 1184 . . . . . 6
6 bnj557.20 . . . . . . 7
7 vex 3112 . . . . . . . 8
87bnj216 33909 . . . . . . 7
96, 8bnj837 33941 . . . . . 6
105, 9anim12i 566 . . . . 5
111, 10sylbir 213 . . . 4
123bnj1254 33990 . . . . . 6
136simp3bi 1013 . . . . . 6
14 bnj551 33921 . . . . . 6
1512, 13, 14syl2an 477 . . . . 5
1615adantl 466 . . . 4
1711, 16jca 532 . . 3
18 bnj256 33880 . . 3
19 df-3an 975 . . 3
2017, 18, 193imtr4i 266 . 2
21 bnj557.28 . . 3
22 bnj557.29 . . 3
23 bnj557.3 . . 3
24 bnj557.16 . . 3
25 bnj557.17 . . 3
26 bnj557.22 . . 3
27 bnj557.25 . . 3
28 bnj557.21 . . 3
29 bnj557.23 . . 3
30 bnj557.24 . . 3
31 bnj557.36 . . 3
3221, 22, 23, 24, 25, 2, 26, 27, 28, 29, 30, 31bnj553 34078 . 2
3320, 32syl 16 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 973   wceq 1395   wcel 1819  wral 2807   cdif 3468   cun 3469  c0 3793  csn 4032  cop 4038  ciun 4332   csuc 4889   wfn 5589  cfv 5594  com 6699   w-bnj17 33860   c-bnj14 33862   w-bnj15 33866 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-8 1821  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-sep 4578  ax-nul 4586  ax-pr 4695  ax-un 6591  ax-reg 8036 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-eu 2287  df-mo 2288  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-uni 4252  df-iun 4334  df-br 4457  df-opab 4516  df-eprel 4800  df-id 4804  df-fr 4847  df-suc 4893  df-xp 5014  df-rel 5015  df-cnv 5016  df-co 5017  df-dm 5018  df-res 5020  df-iota 5557  df-fun 5596  df-fn 5597  df-fv 5602  df-bnj17 33861 This theorem is referenced by:  bnj558  34082
 Copyright terms: Public domain W3C validator