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Theorem psubspi2N 30607
 Description: Property of a projective subspace. (Contributed by NM, 13-Jan-2012.) (New usage is discouraged.)
Hypotheses
Ref Expression
psubspset.l
psubspset.j
psubspset.a
psubspset.s
Assertion
Ref Expression
psubspi2N

Proof of Theorem psubspi2N
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 oveq1 6090 . . . 4
21breq2d 4226 . . 3
3 oveq2 6091 . . . 4
43breq2d 4226 . . 3
52, 4rspc2ev 3062 . 2
6 psubspset.l . . 3
7 psubspset.j . . 3
8 psubspset.a . . 3
9 psubspset.s . . 3
106, 7, 8, 9psubspi 30606 . 2
115, 10sylan2 462 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   w3a 937   wceq 1653   wcel 1726  wrex 2708   class class class wbr 4214  cfv 5456  (class class class)co 6083  cple 13538  cjn 14403  catm 30123  cpsubsp 30355 This theorem is referenced by:  pclclN  30750  pclfinN  30759  pclfinclN  30809 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pow 4379  ax-pr 4405 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 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-opab 4269  df-mpt 4270  df-id 4500  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-iota 5420  df-fun 5458  df-fv 5464  df-ov 6086  df-psubsp 30362
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