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Mirrors > Home > ILE Home > Th. List > qdenval | Unicode version |
Description: Value of the canonical denominator function. (Contributed by Stefan O'Rear, 13-Sep-2014.) |
Ref | Expression |
---|---|
qdenval | denom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2144 | . . . . 5 | |
2 | 1 | anbi2d 459 | . . . 4 |
3 | 2 | riotabidv 5725 | . . 3 |
4 | 3 | fveq2d 5418 | . 2 |
5 | df-denom 11851 | . 2 denom | |
6 | zex 9056 | . . . 4 | |
7 | nnex 8719 | . . . 4 | |
8 | 6, 7 | xpex 4649 | . . 3 |
9 | riotaexg 5727 | . . 3 | |
10 | 2ndexg 6059 | . . 3 | |
11 | 8, 9, 10 | mp2b 8 | . 2 |
12 | 4, 5, 11 | fvmpt 5491 | 1 denom |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 cvv 2681 cxp 4532 cfv 5118 crio 5722 (class class class)co 5767 c1st 6029 c2nd 6030 c1 7614 cdiv 8425 cn 8713 cz 9047 cq 9404 cgcd 11624 denomcdenom 11849 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 ax-cnex 7704 ax-resscn 7705 ax-1re 7707 ax-addrcl 7710 |
This theorem depends on definitions: df-bi 116 df-3or 963 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-sbc 2905 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-int 3767 df-br 3925 df-opab 3985 df-mpt 3986 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-iota 5083 df-fun 5120 df-fn 5121 df-f 5122 df-fo 5124 df-fv 5126 df-riota 5723 df-ov 5770 df-2nd 6032 df-neg 7929 df-inn 8714 df-z 9048 df-denom 11851 |
This theorem is referenced by: qnumdencl 11854 fden 11858 qnumdenbi 11859 |
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