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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 10736 and bj-omex 10737) . (Contributed by BJ, 30-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-2inf | Ind Ind |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2081 | . . . 4 | |
2 | bj-om 10732 | . . . 4 Ind Ind | |
3 | 1, 2 | mpbii 146 | . . 3 Ind Ind |
4 | bj-indeq 10724 | . . . . 5 Ind Ind | |
5 | sseq1 3020 | . . . . . . 7 | |
6 | 5 | imbi2d 228 | . . . . . 6 Ind Ind |
7 | 6 | albidv 1745 | . . . . 5 Ind Ind |
8 | 4, 7 | anbi12d 456 | . . . 4 Ind Ind Ind Ind |
9 | 8 | spcegv 2686 | . . 3 Ind Ind Ind Ind |
10 | 3, 9 | mpd 13 | . 2 Ind Ind |
11 | vex 2604 | . . . . . 6 | |
12 | bj-om 10732 | . . . . . 6 Ind Ind | |
13 | 11, 12 | ax-mp 7 | . . . . 5 Ind Ind |
14 | 13 | biimpri 131 | . . . 4 Ind Ind |
15 | 14 | eximi 1531 | . . 3 Ind Ind |
16 | isset 2605 | . . 3 | |
17 | 15, 16 | sylibr 132 | . 2 Ind Ind |
18 | 10, 17 | impbii 124 | 1 Ind Ind |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wceq 1284 wex 1421 wcel 1433 cvv 2601 wss 2973 com 4331 Ind wind 10721 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-nul 3904 ax-pr 3964 ax-un 4188 ax-bd0 10604 ax-bdor 10607 ax-bdex 10610 ax-bdeq 10611 ax-bdel 10612 ax-bdsb 10613 ax-bdsep 10675 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-rab 2357 df-v 2603 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-nul 3252 df-sn 3404 df-pr 3405 df-uni 3602 df-int 3637 df-suc 4126 df-iom 4332 df-bdc 10632 df-bj-ind 10722 |
This theorem is referenced by: bj-omex 10737 |
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