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Theorem psubssat 33737
 Description: A projective subspace consists of atoms. (Contributed by NM, 4-Nov-2011.)
Hypotheses
Ref Expression
atpsub.a
atpsub.s
Assertion
Ref Expression
psubssat

Proof of Theorem psubssat
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eqid 2454 . . 3
2 eqid 2454 . . 3
3 atpsub.a . . 3
4 atpsub.s . . 3
51, 2, 3, 4ispsubsp 33728 . 2
65simprbda 623 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1370   wcel 1758  wral 2799   wss 3437   class class class wbr 4401  cfv 5527  (class class class)co 6201  cple 14365  cjn 15234  catm 33247  cpsubsp 33479 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4522  ax-nul 4530  ax-pow 4579  ax-pr 4640 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2804  df-rex 2805  df-rab 2808  df-v 3080  df-sbc 3295  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-nul 3747  df-if 3901  df-pw 3971  df-sn 3987  df-pr 3989  df-op 3993  df-uni 4201  df-br 4402  df-opab 4460  df-mpt 4461  df-id 4745  df-xp 4955  df-rel 4956  df-cnv 4957  df-co 4958  df-dm 4959  df-iota 5490  df-fun 5529  df-fv 5535  df-ov 6204  df-psubsp 33486 This theorem is referenced by:  psubatN  33738  paddidm  33824  paddclN  33825  paddss  33828  pmodlem1  33829  pmod1i  33831  pmodl42N  33834  elpcliN  33876  pclidN  33879  pclbtwnN  33880  pclunN  33881  pclun2N  33882  pclfinN  33883  polssatN  33891  psubclsubN  33923
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