Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-inf2vn2 | Unicode version |
Description: A sufficient condition for to be a set; unbounded version of bj-inf2vn 13161. (Contributed by BJ, 8-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-inf2vn2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-inf2vnlem1 13157 | . . 3 Ind | |
2 | bi1 117 | . . . . . . 7 | |
3 | 2 | alimi 1431 | . . . . . 6 |
4 | df-ral 2419 | . . . . . 6 | |
5 | 3, 4 | sylibr 133 | . . . . 5 |
6 | bj-inf2vnlem4 13160 | . . . . 5 Ind | |
7 | 5, 6 | syl 14 | . . . 4 Ind |
8 | 7 | alrimiv 1846 | . . 3 Ind |
9 | 1, 8 | jca 304 | . 2 Ind Ind |
10 | bj-om 13124 | . 2 Ind Ind | |
11 | 9, 10 | syl5ibr 155 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wo 697 wal 1329 wceq 1331 wcel 1480 wral 2414 wrex 2415 wss 3066 c0 3358 csuc 4282 com 4499 Ind wind 13113 |
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-nul 4049 ax-pr 4126 ax-un 4350 ax-setind 4447 ax-bd0 13000 ax-bdor 13003 ax-bdex 13006 ax-bdeq 13007 ax-bdel 13008 ax-bdsb 13009 ax-bdsep 13071 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-nul 3359 df-sn 3528 df-pr 3529 df-uni 3732 df-int 3767 df-suc 4288 df-iom 4500 df-bdc 13028 df-bj-ind 13114 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |