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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-2inf | Unicode version |
Description: Two formulations of the axiom of infinity (see ax-infvn 13128 and bj-omex 13129) . (Contributed by BJ, 30-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-2inf | Ind Ind |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2137 | . . . 4 | |
2 | bj-om 13124 | . . . 4 Ind Ind | |
3 | 1, 2 | mpbii 147 | . . 3 Ind Ind |
4 | bj-indeq 13116 | . . . . 5 Ind Ind | |
5 | sseq1 3115 | . . . . . . 7 | |
6 | 5 | imbi2d 229 | . . . . . 6 Ind Ind |
7 | 6 | albidv 1796 | . . . . 5 Ind Ind |
8 | 4, 7 | anbi12d 464 | . . . 4 Ind Ind Ind Ind |
9 | 8 | spcegv 2769 | . . 3 Ind Ind Ind Ind |
10 | 3, 9 | mpd 13 | . 2 Ind Ind |
11 | vex 2684 | . . . . . 6 | |
12 | bj-om 13124 | . . . . . 6 Ind Ind | |
13 | 11, 12 | ax-mp 5 | . . . . 5 Ind Ind |
14 | 13 | biimpri 132 | . . . 4 Ind Ind |
15 | 14 | eximi 1579 | . . 3 Ind Ind |
16 | isset 2687 | . . 3 | |
17 | 15, 16 | sylibr 133 | . 2 Ind Ind |
18 | 10, 17 | impbii 125 | 1 Ind Ind |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wceq 1331 wex 1468 wcel 1480 cvv 2681 wss 3066 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-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: bj-omex 13129 |
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