Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > enq0ex | Unicode version |
Description: The equivalence relation for positive fractions exists. (Contributed by Jim Kingdon, 18-Nov-2019.) |
Ref | Expression |
---|---|
enq0ex | ~Q0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | omex 4552 | . . . 4 | |
2 | niex 7232 | . . . 4 | |
3 | 1, 2 | xpex 4701 | . . 3 |
4 | 3, 3 | xpex 4701 | . 2 |
5 | df-enq0 7344 | . . 3 ~Q0 | |
6 | opabssxp 4660 | . . 3 | |
7 | 5, 6 | eqsstri 3160 | . 2 ~Q0 |
8 | 4, 7 | ssexi 4102 | 1 ~Q0 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1335 wex 1472 wcel 2128 cvv 2712 cop 3563 copab 4024 com 4549 cxp 4584 (class class class)co 5824 comu 6361 cnpi 7192 ~Q0 ceq0 7206 |
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 604 ax-in2 605 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-iinf 4547 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-dif 3104 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-opab 4026 df-iom 4550 df-xp 4592 df-ni 7224 df-enq0 7344 |
This theorem is referenced by: nqnq0 7361 addnnnq0 7369 mulnnnq0 7370 addclnq0 7371 mulclnq0 7372 prarloclemcalc 7422 |
Copyright terms: Public domain | W3C validator |