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Theorem lshpne 29717
 Description: A hyperplane is not equal to the vector space. (Contributed by NM, 4-Jul-2014.)
Hypotheses
Ref Expression
lshpne.v
lshpne.h LSHyp
lshpne.w
lshpne.u
Assertion
Ref Expression
lshpne

Proof of Theorem lshpne
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 lshpne.u . . 3
2 lshpne.w . . . 4
3 lshpne.v . . . . 5
4 eqid 2435 . . . . 5
5 eqid 2435 . . . . 5
6 lshpne.h . . . . 5 LSHyp
73, 4, 5, 6islshp 29714 . . . 4
82, 7syl 16 . . 3
91, 8mpbid 202 . 2
109simp2d 970 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   w3a 936   wceq 1652   wcel 1725   wne 2598  wrex 2698   cun 3310  csn 3806  cfv 5446  cbs 13461  clmod 15942  clss 16000  clspn 16039  LSHypclsh 29710 This theorem is referenced by:  lshpnel  29718  lshpcmp  29723  lkrshp3  29841  lkrshp4  29843  dochshpncl  32119  dochlkr  32120  dochkrshp  32121  dochsatshpb  32187 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-iota 5410  df-fun 5448  df-fv 5454  df-lshyp 29712
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