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Theorem atpsubN 29942
 Description: The set of all atoms is a projective subspace. Remark below Definition 15.1 of [MaedaMaeda] p. 61. (Contributed by NM, 13-Oct-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
atpsub.a
atpsub.s
Assertion
Ref Expression
atpsubN

Proof of Theorem atpsubN
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ssid 3197 . . 3
2 ax-1 5 . . . . 5
32rgen 2608 . . . 4
43rgen2w 2611 . . 3
51, 4pm3.2i 441 . 2
6 eqid 2283 . . 3
7 eqid 2283 . . 3
8 atpsub.a . . 3
9 atpsub.s . . 3
106, 7, 8, 9ispsubsp 29934 . 2
115, 10mpbiri 224 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   wceq 1623   wcel 1684  wral 2543   wss 3152   class class class wbr 4023  cfv 5255  (class class class)co 5858  cple 13215  cjn 14078  catm 29453  cpsubsp 29685 This theorem is referenced by:  pclvalN  30079  pclclN  30080 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pow 4188  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-pw 3627  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-mpt 4079  df-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-iota 5219  df-fun 5257  df-fv 5263  df-ov 5861  df-psubsp 29692
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