Mathbox for Norm Megill < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  pmap1N Unicode version

Theorem pmap1N 29956
 Description: Value of the projective map of a Hilbert lattice at lattice unit. Part of Theorem 15.5.1 of [MaedaMaeda] p. 62. (Contributed by NM, 22-Oct-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
pmap1.u
pmap1.a
pmap1.m
Assertion
Ref Expression
pmap1N

Proof of Theorem pmap1N
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqid 2283 . . . 4
2 pmap1.u . . . 4
31, 2op1cl 29375 . . 3
4 eqid 2283 . . . 4
5 pmap1.a . . . 4
6 pmap1.m . . . 4
71, 4, 5, 6pmapval 29946 . . 3
83, 7mpdan 649 . 2
91, 5atbase 29479 . . . . 5
101, 4, 2ople1 29381 . . . . 5
119, 10sylan2 460 . . . 4
1211ralrimiva 2626 . . 3
13 rabid2 2717 . . 3
1412, 13sylibr 203 . 2
158, 14eqtr4d 2318 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1623   wcel 1684  wral 2543  crab 2547   class class class wbr 4023  cfv 5255  cbs 13148  cple 13215  cp1 14144  cops 29362  catm 29453  cpmap 29686 This theorem is referenced by:  pmapglb2N  29960  pmapglb2xN  29961 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-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-rep 4131  ax-sep 4141  ax-nul 4149  ax-pow 4188  ax-pr 4214  ax-un 4512 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-nel 2449  df-ral 2548  df-rex 2549  df-reu 2550  df-rab 2552  df-v 2790  df-sbc 2992  df-csb 3082  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-iun 3907  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-rn 4700  df-res 4701  df-ima 4702  df-iota 5219  df-fun 5257  df-fn 5258  df-f 5259  df-f1 5260  df-fo 5261  df-f1o 5262  df-fv 5263  df-ov 5861  df-undef 6298  df-riota 6304  df-lub 14108  df-p1 14146  df-oposet 29366  df-ats 29457  df-pmap 29693
 Copyright terms: Public domain W3C validator