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Theorem atpsubN 29209
 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
Dummy variables are mutually distinct and distinct from all other variables.

Proof of Theorem atpsubN
StepHypRef Expression
1 ssid 3198 . . 3
2 ax-1 7 . . . . 5
32rgen 2609 . . . 4
43rgen2w 2612 . . 3
51, 4pm3.2i 443 . 2
6 eqid 2284 . . 3
7 eqid 2284 . . 3
8 atpsub.a . . 3
9 atpsub.s . . 3
106, 7, 8, 9ispsubsp 29201 . 2
115, 10mpbiri 226 1
 Colors of variables: wff set class Syntax hints:   wi 6   wa 360   wceq 1624   wcel 1685  wral 2544   wss 3153   class class class wbr 4024  cfv 5221  (class class class)co 5819  cple 13209  cjn 14072  catm 28720  cpsubsp 28952 This theorem is referenced by:  pclvalN  29346  pclclN  29347 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-13 1687  ax-14 1689  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1867  ax-ext 2265  ax-sep 4142  ax-nul 4150  ax-pow 4187  ax-pr 4213  ax-un 4511 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 938  df-tru 1312  df-ex 1530  df-nf 1533  df-sb 1632  df-eu 2148  df-mo 2149  df-clab 2271  df-cleq 2277  df-clel 2280  df-nfc 2409  df-ne 2449  df-ral 2549  df-rex 2550  df-rab 2553  df-v 2791  df-sbc 2993  df-dif 3156  df-un 3158  df-in 3160  df-ss 3167  df-nul 3457  df-if 3567  df-pw 3628  df-sn 3647  df-pr 3648  df-op 3650  df-uni 3829  df-br 4025  df-opab 4079  df-mpt 4080  df-id 4308  df-xp 4694  df-rel 4695  df-cnv 4696  df-co 4697  df-dm 4698  df-rn 4699  df-res 4700  df-ima 4701  df-fun 5223  df-fv 5229  df-ov 5822  df-psubsp 28959
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