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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 2146 | . . . . 5 | |
2 | 1 | anbi2d 459 | . . . 4 |
3 | 2 | riotabidv 5732 | . . 3 |
4 | 3 | fveq2d 5425 | . 2 |
5 | df-denom 11862 | . 2 denom | |
6 | zex 9063 | . . . 4 | |
7 | nnex 8726 | . . . 4 | |
8 | 6, 7 | xpex 4654 | . . 3 |
9 | riotaexg 5734 | . . 3 | |
10 | 2ndexg 6066 | . . 3 | |
11 | 8, 9, 10 | mp2b 8 | . 2 |
12 | 4, 5, 11 | fvmpt 5498 | 1 denom |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 cvv 2686 cxp 4537 cfv 5123 crio 5729 (class class class)co 5774 c1st 6036 c2nd 6037 c1 7621 cdiv 8432 cn 8720 cz 9054 cq 9411 cgcd 11635 denomcdenom 11860 |
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 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 ax-cnex 7711 ax-resscn 7712 ax-1re 7714 ax-addrcl 7717 |
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 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-rab 2425 df-v 2688 df-sbc 2910 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-int 3772 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-fo 5129 df-fv 5131 df-riota 5730 df-ov 5777 df-2nd 6039 df-neg 7936 df-inn 8721 df-z 9055 df-denom 11862 |
This theorem is referenced by: qnumdencl 11865 fden 11869 qnumdenbi 11870 |
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