Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1388 Structured version   Visualization version   Unicode version

Theorem bnj1388 29914
 Description: Technical lemma for bnj60 29943. 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
bnj1388.1
bnj1388.2
bnj1388.3
bnj1388.4
bnj1388.5
bnj1388.6
bnj1388.7
bnj1388.8
Assertion
Ref Expression
bnj1388
Distinct variable groups:   ,,   ,   ,   ,,   ,,   ,   ,   ,
Allowed substitution hints:   (,,)   (,,,)   (,,)   (,)   (,,)   (,,,)   (,,)   (,)   (,,,)   (,,,)   (,,,)

Proof of Theorem bnj1388
StepHypRef Expression
1 bnj1388.7 . . 3
2 nfv 1769 . . . 4
3 nfv 1769 . . . 4
4 nfra1 2785 . . . 4
52, 3, 4nf3an 2033 . . 3
61, 5nfxfr 1704 . 2
7 bnj1152 29879 . . . . . 6
87simplbi 467 . . . . 5
98adantl 473 . . . 4
107biimpi 199 . . . . . . . . 9
1110adantl 473 . . . . . . . 8
1211simprd 470 . . . . . . 7
131simp3bi 1047 . . . . . . . 8
1413adantr 472 . . . . . . 7
15 df-ral 2761 . . . . . . . . 9
16 con2b 341 . . . . . . . . . 10
1716albii 1699 . . . . . . . . 9
1815, 17bitri 257 . . . . . . . 8
19 sp 1957 . . . . . . . . 9
2019impcom 437 . . . . . . . 8
2118, 20sylan2b 483 . . . . . . 7
2212, 14, 21syl2anc 673 . . . . . 6
23 bnj1388.5 . . . . . . . 8
2423eleq2i 2541 . . . . . . 7
25 nfcv 2612 . . . . . . . 8
26 nfcv 2612 . . . . . . . 8
27 bnj1388.8 . . . . . . . . . . 11
28 nfsbc1v 3275 . . . . . . . . . . 11
2927, 28nfxfr 1704 . . . . . . . . . 10
3029nfex 2050 . . . . . . . . 9
3130nfn 2003 . . . . . . . 8
32 sbceq1a 3266 . . . . . . . . . . 11
3332, 27syl6bbr 271 . . . . . . . . . 10
3433exbidv 1776 . . . . . . . . 9
3534notbid 301 . . . . . . . 8
3625, 26, 31, 35elrabf 3182 . . . . . . 7
3724, 36bitri 257 . . . . . 6
3822, 37sylnib 311 . . . . 5
39 iman 431 . . . . 5
4038, 39sylibr 217 . . . 4
419, 40mpd 15 . . 3
4241ex 441 . 2
436, 42ralrimi 2800 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 189   wa 376   w3a 1007  wal 1450   wceq 1452  wex 1671   wcel 1904  cab 2457   wne 2641  wral 2756  wrex 2757  crab 2760  wsbc 3255   cun 3388   wss 3390  c0 3722  csn 3959  cop 3965   class class class wbr 4395   cdm 4839   cres 4841   wfn 5584  cfv 5589   c-bnj14 29565   w-bnj15 29569   c-bnj18 29571 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-rab 2765  df-v 3033  df-sbc 3256  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-br 4396  df-bnj14 29566 This theorem is referenced by:  bnj1398  29915  bnj1489  29937
 Copyright terms: Public domain W3C validator