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Mirrors > Home > MPE Home > Th. List > Mathboxes > elpell1qr | Structured version Visualization version Unicode version |
Description: Membership in a first-quadrant Pell solution set. (Contributed by Stefan O'Rear, 17-Sep-2014.) |
Ref | Expression |
---|---|
elpell1qr | ◻NN Pell1QR |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pell1qrval 37410 | . . 3 ◻NN Pell1QR | |
2 | 1 | eleq2d 2687 | . 2 ◻NN Pell1QR |
3 | eqeq1 2626 | . . . . 5 | |
4 | 3 | anbi1d 741 | . . . 4 |
5 | 4 | 2rexbidv 3057 | . . 3 |
6 | 5 | elrab 3363 | . 2 |
7 | 2, 6 | syl6bb 276 | 1 ◻NN Pell1QR |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 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 cexp 12860 csqrt 13973 ◻NNcsquarenn 37400 Pell1QRcpell1qr 37401 |
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-pell1qr 37406 |
This theorem is referenced by: pell1qrss14 37432 pell14qrdich 37433 pell1qrge1 37434 pell1qr1 37435 pell1qrgap 37438 pellqrexplicit 37441 |
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