Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > sqrtrval | Unicode version |
Description: Value of square root function. (Contributed by Jim Kingdon, 23-Aug-2020.) |
Ref | Expression |
---|---|
sqrtrval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq2 2127 | . . . 4 | |
2 | 1 | anbi1d 460 | . . 3 |
3 | 2 | riotabidv 5700 | . 2 |
4 | df-rsqrt 10738 | . 2 | |
5 | reex 7722 | . . 3 | |
6 | riotaexg 5702 | . . 3 | |
7 | 5, 6 | ax-mp 5 | . 2 |
8 | 3, 4, 7 | fvmpt 5466 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 wcel 1465 cvv 2660 class class class wbr 3899 cfv 5093 crio 5697 (class class class)co 5742 cr 7587 cc0 7588 cle 7769 c2 8739 cexp 10260 csqrt 10736 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-un 4325 ax-cnex 7679 ax-resscn 7680 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-sbc 2883 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-mpt 3961 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-iota 5058 df-fun 5095 df-fv 5101 df-riota 5698 df-rsqrt 10738 |
This theorem is referenced by: sqrt0 10744 resqrtcl 10769 rersqrtthlem 10770 sqrtsq 10784 |
Copyright terms: Public domain | W3C validator |