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Mirrors > Home > ILE Home > Th. List > 1nq | Unicode version |
Description: The positive fraction 'one'. (Contributed by NM, 29-Oct-1995.) |
Ref | Expression |
---|---|
1nq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1pi 7292 |
. . . 4
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2 | opelxpi 4654 |
. . . 4
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3 | 1, 1, 2 | mp2an 426 |
. . 3
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4 | enqex 7337 |
. . . 4
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5 | 4 | ecelqsi 6582 |
. . 3
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6 | 3, 5 | ax-mp 5 |
. 2
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7 | df-1nqqs 7328 |
. 2
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8 | df-nqqs 7325 |
. 2
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9 | 6, 7, 8 | 3eltr4i 2259 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-nul 4126 ax-pow 4171 ax-pr 4205 ax-un 4429 ax-iinf 4583 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-nul 3423 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-int 3843 df-br 4001 df-opab 4062 df-suc 4367 df-iom 4586 df-xp 4628 df-cnv 4630 df-dm 4632 df-rn 4633 df-res 4634 df-ima 4635 df-1o 6410 df-ec 6530 df-qs 6534 df-ni 7281 df-enq 7324 df-nqqs 7325 df-1nqqs 7328 |
This theorem is referenced by: recmulnqg 7368 rec1nq 7372 ltaddnq 7384 halfnqq 7387 addnqprllem 7504 addnqprulem 7505 1pr 7531 addnqpr1 7539 appdivnq 7540 1idprl 7567 1idpru 7568 recexprlemm 7601 recexprlem1ssl 7610 recexprlem1ssu 7611 cauappcvgprlemm 7622 caucvgprlemm 7645 caucvgprprlemmu 7672 suplocexprlemmu 7695 |
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