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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 2164 | . . . . 5 | |
2 | 1 | anbi2d 460 | . . . 4 |
3 | 2 | riotabidv 5782 | . . 3 |
4 | 3 | fveq2d 5472 | . 2 |
5 | df-denom 12059 | . 2 denom | |
6 | zex 9176 | . . . 4 | |
7 | nnex 8839 | . . . 4 | |
8 | 6, 7 | xpex 4701 | . . 3 |
9 | riotaexg 5784 | . . 3 | |
10 | 2ndexg 6116 | . . 3 | |
11 | 8, 9, 10 | mp2b 8 | . 2 |
12 | 4, 5, 11 | fvmpt 5545 | 1 denom |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wcel 2128 cvv 2712 cxp 4584 cfv 5170 crio 5779 (class class class)co 5824 c1st 6086 c2nd 6087 c1 7733 cdiv 8545 cn 8833 cz 9167 cq 9528 cgcd 11829 denomcdenom 12057 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 ax-un 4393 ax-cnex 7823 ax-resscn 7824 ax-1re 7826 ax-addrcl 7829 |
This theorem depends on definitions: df-bi 116 df-3or 964 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-rab 2444 df-v 2714 df-sbc 2938 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-int 3808 df-br 3966 df-opab 4026 df-mpt 4027 df-id 4253 df-xp 4592 df-rel 4593 df-cnv 4594 df-co 4595 df-dm 4596 df-rn 4597 df-iota 5135 df-fun 5172 df-fn 5173 df-f 5174 df-fo 5176 df-fv 5178 df-riota 5780 df-ov 5827 df-2nd 6089 df-neg 8049 df-inn 8834 df-z 9168 df-denom 12059 |
This theorem is referenced by: qnumdencl 12062 fden 12066 qnumdenbi 12067 |
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