Mathbox for Norm Megill < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  0psubN Structured version   Unicode version

Theorem 0psubN 30720
 Description: The empty set is a projective subspace. Remark below Definition 15.1 of [MaedaMaeda] p. 61. (Contributed by NM, 13-Oct-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
0psub.s
Assertion
Ref Expression
0psubN

Proof of Theorem 0psubN
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 0ss 3644 . . 3
2 ral0 3760 . . 3
31, 2pm3.2i 443 . 2
4 eqid 2443 . . 3
5 eqid 2443 . . 3
6 eqid 2443 . . 3
7 0psub.s . . 3
84, 5, 6, 7ispsubsp 30716 . 2
93, 8mpbiri 226 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1654   wcel 1728  wral 2712   wss 3309  c0 3616   class class class wbr 4243  cfv 5489  (class class class)co 6117  cple 13574  cjn 14439  catm 30235  cpsubsp 30467 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-14 1732  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424  ax-sep 4361  ax-nul 4369  ax-pow 4412  ax-pr 4438 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-eu 2292  df-mo 2293  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ne 2608  df-ral 2717  df-rex 2718  df-rab 2721  df-v 2967  df-sbc 3171  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-nul 3617  df-if 3768  df-pw 3830  df-sn 3849  df-pr 3850  df-op 3852  df-uni 4045  df-br 4244  df-opab 4298  df-mpt 4299  df-id 4533  df-xp 4919  df-rel 4920  df-cnv 4921  df-co 4922  df-dm 4923  df-iota 5453  df-fun 5491  df-fv 5497  df-ov 6120  df-psubsp 30474
 Copyright terms: Public domain W3C validator