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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 7309 |
. . . 4
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2 | opelxpi 4656 |
. . . 4
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3 | 1, 1, 2 | mp2an 426 |
. . 3
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4 | enqex 7354 |
. . . 4
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5 | 4 | ecelqsi 6584 |
. . 3
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6 | 3, 5 | ax-mp 5 |
. 2
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7 | df-1nqqs 7345 |
. 2
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8 | df-nqqs 7342 |
. 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 4119 ax-nul 4127 ax-pow 4172 ax-pr 4207 ax-un 4431 ax-iinf 4585 |
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 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3809 df-int 3844 df-br 4002 df-opab 4063 df-suc 4369 df-iom 4588 df-xp 4630 df-cnv 4632 df-dm 4634 df-rn 4635 df-res 4636 df-ima 4637 df-1o 6412 df-ec 6532 df-qs 6536 df-ni 7298 df-enq 7341 df-nqqs 7342 df-1nqqs 7345 |
This theorem is referenced by: recmulnqg 7385 rec1nq 7389 ltaddnq 7401 halfnqq 7404 addnqprllem 7521 addnqprulem 7522 1pr 7548 addnqpr1 7556 appdivnq 7557 1idprl 7584 1idpru 7585 recexprlemm 7618 recexprlem1ssl 7627 recexprlem1ssu 7628 cauappcvgprlemm 7639 caucvgprlemm 7662 caucvgprprlemmu 7689 suplocexprlemmu 7712 |
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