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Mirrors > Home > MPE Home > Th. List > Mathboxes > pell14qrval | Structured version Visualization version Unicode version |
Description: Value of the set of positive Pell solutions. (Contributed by Stefan O'Rear, 17-Sep-2014.) |
Ref | Expression |
---|---|
pell14qrval | ◻NN Pell14QR |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq2 6191 | . . . . . . . 8 | |
2 | 1 | oveq1d 6665 | . . . . . . 7 |
3 | 2 | oveq2d 6666 | . . . . . 6 |
4 | 3 | eqeq2d 2632 | . . . . 5 |
5 | oveq1 6657 | . . . . . . 7 | |
6 | 5 | oveq2d 6666 | . . . . . 6 |
7 | 6 | eqeq1d 2624 | . . . . 5 |
8 | 4, 7 | anbi12d 747 | . . . 4 |
9 | 8 | 2rexbidv 3057 | . . 3 |
10 | 9 | rabbidv 3189 | . 2 |
11 | df-pell14qr 37407 | . 2 Pell14QR ◻NN | |
12 | reex 10027 | . . 3 | |
13 | 12 | rabex 4813 | . 2 |
14 | 10, 11, 13 | fvmpt 6282 | 1 ◻NN Pell14QR |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 wrex 2913 crab 2916 cdif 3571 cfv 5888 (class class class)co 6650 cr 9935 c1 9937 caddc 9939 cmul 9941 cmin 10266 cn 11020 c2 11070 cn0 11292 cz 11377 cexp 12860 csqrt 13973 ◻NNcsquarenn 37400 Pell14QRcpell14qr 37403 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 ax-cnex 9992 ax-resscn 9993 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-ov 6653 df-pell14qr 37407 |
This theorem is referenced by: elpell14qr 37413 rmxyelqirr 37475 |
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