Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > gtnqex | Unicode version |
Description: The class of rationals greater than a given rational is a set. (Contributed by Jim Kingdon, 13-Dec-2019.) |
Ref | Expression |
---|---|
gtnqex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nqex 7164 | . 2 | |
2 | ltrelnq 7166 | . . . . 5 | |
3 | 2 | brel 4586 | . . . 4 |
4 | 3 | simprd 113 | . . 3 |
5 | 4 | abssi 3167 | . 2 |
6 | 1, 5 | ssexi 4061 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 cab 2123 cvv 2681 class class class wbr 3924 cnq 7081 cltq 7086 |
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-in1 603 ax-in2 604 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-coll 4038 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 ax-iinf 4497 |
This theorem depends on definitions: df-bi 116 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-reu 2421 df-rab 2423 df-v 2683 df-sbc 2905 df-csb 2999 df-dif 3068 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-iun 3810 df-br 3925 df-opab 3985 df-mpt 3986 df-id 4210 df-iom 4500 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-res 4546 df-ima 4547 df-iota 5083 df-fun 5120 df-fn 5121 df-f 5122 df-f1 5123 df-fo 5124 df-f1o 5125 df-fv 5126 df-qs 6428 df-ni 7105 df-nqqs 7149 df-ltnqqs 7154 |
This theorem is referenced by: nqprl 7352 nqpru 7353 1prl 7356 1pru 7357 addnqprlemrl 7358 addnqprlemru 7359 addnqprlemfl 7360 addnqprlemfu 7361 mulnqprlemrl 7374 mulnqprlemru 7375 mulnqprlemfl 7376 mulnqprlemfu 7377 ltnqpr 7394 ltnqpri 7395 archpr 7444 cauappcvgprlemladdfu 7455 cauappcvgprlemladdfl 7456 cauappcvgprlem2 7461 caucvgprlemladdfu 7478 caucvgprlem2 7481 caucvgprprlemopu 7500 suplocexprlemloc 7522 |
Copyright terms: Public domain | W3C validator |