Mathbox for Stefan O'Rear < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  pell1234qrval Structured version   Unicode version

Theorem pell1234qrval 26951
 Description: Value of the set of general Pell solutions. (Contributed by Stefan O'Rear, 17-Sep-2014.)
Assertion
Ref Expression
pell1234qrval NN Pell1234QR
Distinct variable group:   ,,,

Proof of Theorem pell1234qrval
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fveq2 5757 . . . . . . . 8
21oveq1d 6125 . . . . . . 7
32oveq2d 6126 . . . . . 6
43eqeq2d 2453 . . . . 5
5 oveq1 6117 . . . . . . 7
65oveq2d 6126 . . . . . 6
76eqeq1d 2450 . . . . 5
84, 7anbi12d 693 . . . 4
982rexbidv 2754 . . 3
109rabbidv 2954 . 2
11 df-pell1234qr 26945 . 2 Pell1234QR NN
12 reex 9112 . . 3
1312rabex 4383 . 2
1410, 11, 13fvmpt 5835 1 NN Pell1234QR
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1727  wrex 2712  crab 2715   cdif 3303  cfv 5483  (class class class)co 6110  cr 9020  c1 9022   caddc 9024   cmul 9026   cmin 9322  cn 10031  c2 10080  cz 10313  cexp 11413  csqr 12069  ◻NNcsquarenn 26937  Pell1234QRcpell1234qr 26939 This theorem is referenced by:  elpell1234qr  26952 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 1627  ax-9 1668  ax-8 1689  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-sep 4355  ax-nul 4363  ax-pr 4432  ax-cnex 9077  ax-resscn 9078 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 2291  df-mo 2292  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-rex 2717  df-rab 2720  df-v 2964  df-sbc 3168  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-uni 4040  df-br 4238  df-opab 4292  df-mpt 4293  df-id 4527  df-xp 4913  df-rel 4914  df-cnv 4915  df-co 4916  df-dm 4917  df-iota 5447  df-fun 5485  df-fv 5491  df-ov 6113  df-pell1234qr 26945
 Copyright terms: Public domain W3C validator