Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2177 | . . . . 5 | |
2 | 1 | anbi2d 461 | . . . 4 |
3 | 2 | riotabidv 5811 | . . 3 |
4 | 3 | fveq2d 5500 | . 2 |
5 | df-denom 12138 | . 2 denom | |
6 | zex 9221 | . . . 4 | |
7 | nnex 8884 | . . . 4 | |
8 | 6, 7 | xpex 4726 | . . 3 |
9 | riotaexg 5813 | . . 3 | |
10 | 2ndexg 6147 | . . 3 | |
11 | 8, 9, 10 | mp2b 8 | . 2 |
12 | 4, 5, 11 | fvmpt 5573 | 1 denom |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wcel 2141 cvv 2730 cxp 4609 cfv 5198 crio 5808 (class class class)co 5853 c1st 6117 c2nd 6118 c1 7775 cdiv 8589 cn 8878 cz 9212 cq 9578 cgcd 11897 denomcdenom 12136 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 ax-un 4418 ax-cnex 7865 ax-resscn 7866 ax-1re 7868 ax-addrcl 7871 |
This theorem depends on definitions: df-bi 116 df-3or 974 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-rab 2457 df-v 2732 df-sbc 2956 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-int 3832 df-br 3990 df-opab 4051 df-mpt 4052 df-id 4278 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-rn 4622 df-iota 5160 df-fun 5200 df-fn 5201 df-f 5202 df-fo 5204 df-fv 5206 df-riota 5809 df-ov 5856 df-2nd 6120 df-neg 8093 df-inn 8879 df-z 9213 df-denom 12138 |
This theorem is referenced by: qnumdencl 12141 fden 12145 qnumdenbi 12146 |
Copyright terms: Public domain | W3C validator |