Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > fiprc | Unicode version |
Description: The class of finite sets is a proper class. (Contributed by Jeff Hankins, 3-Oct-2008.) |
Ref | Expression |
---|---|
fiprc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snnex 4339 | . 2 | |
2 | vex 2663 | . . . . . . . . 9 | |
3 | snfig 6676 | . . . . . . . . 9 | |
4 | 2, 3 | ax-mp 5 | . . . . . . . 8 |
5 | eleq1 2180 | . . . . . . . 8 | |
6 | 4, 5 | mpbiri 167 | . . . . . . 7 |
7 | 6 | exlimiv 1562 | . . . . . 6 |
8 | 7 | abssi 3142 | . . . . 5 |
9 | ssexg 4037 | . . . . 5 | |
10 | 8, 9 | mpan 420 | . . . 4 |
11 | 10 | con3i 606 | . . 3 |
12 | df-nel 2381 | . . 3 | |
13 | df-nel 2381 | . . 3 | |
14 | 11, 12, 13 | 3imtr4i 200 | . 2 |
15 | 1, 14 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wceq 1316 wex 1453 wcel 1465 cab 2103 wnel 2380 cvv 2660 wss 3041 csn 3497 cfn 6602 |
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 588 ax-in2 589 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-nul 4024 ax-pow 4068 ax-pr 4101 ax-un 4325 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 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-nel 2381 df-ral 2398 df-rex 2399 df-v 2662 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-int 3742 df-br 3900 df-opab 3960 df-id 4185 df-suc 4263 df-iom 4475 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-fun 5095 df-fn 5096 df-f 5097 df-f1 5098 df-fo 5099 df-f1o 5100 df-1o 6281 df-en 6603 df-fin 6605 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |