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Theorem pointsetN 30475
 Description: The set of points in a Hilbert lattice. (Contributed by NM, 2-Oct-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
pointset.a
pointset.p
Assertion
Ref Expression
pointsetN
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,)   (,)   ()

Proof of Theorem pointsetN
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elex 2956 . 2
2 pointset.p . . 3
3 fveq2 5720 . . . . . . 7
4 pointset.a . . . . . . 7
53, 4syl6eqr 2485 . . . . . 6
65rexeqdv 2903 . . . . 5
76abbidv 2549 . . . 4
8 df-pointsN 30236 . . . 4
9 fvex 5734 . . . . . 6
104, 9eqeltri 2505 . . . . 5
1110abrexex 5975 . . . 4
127, 8, 11fvmpt 5798 . . 3
132, 12syl5eq 2479 . 2
141, 13syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  cab 2421  wrex 2698  cvv 2948  csn 3806  cfv 5446  catm 29998  cpointsN 30229 This theorem is referenced by:  ispointN  30476 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-rep 4312  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-un 4693 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-reu 2704  df-rab 2706  df-v 2950  df-sbc 3154  df-csb 3244  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-iota 5410  df-fun 5448  df-fn 5449  df-f 5450  df-f1 5451  df-fo 5452  df-f1o 5453  df-fv 5454  df-pointsN 30236
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