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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-omex2 | Unicode version |
Description: Using bounded set induction and the strong axiom of infinity, is a set, that is, we recover ax-infvn 13516 (see bj-2inf 13513 for the equivalence of the latter with bj-omex 13517). (Contributed by BJ, 8-Dec-2019.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bj-omex2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-inf2 13551 | . . 3 | |
2 | vex 2715 | . . . 4 | |
3 | bdcv 13423 | . . . . 5 BOUNDED | |
4 | 3 | bj-inf2vn 13549 | . . . 4 |
5 | 2, 4 | ax-mp 5 | . . 3 |
6 | 1, 5 | eximii 1582 | . 2 |
7 | 6 | issetri 2721 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wo 698 wal 1333 wceq 1335 wcel 2128 wrex 2436 cvv 2712 c0 3394 csuc 4325 com 4549 |
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-nul 4090 ax-pr 4169 ax-un 4393 ax-bd0 13388 ax-bdim 13389 ax-bdor 13391 ax-bdex 13394 ax-bdeq 13395 ax-bdel 13396 ax-bdsb 13397 ax-bdsep 13459 ax-bdsetind 13543 ax-inf2 13551 |
This theorem depends on definitions: df-bi 116 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-rab 2444 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3395 df-sn 3566 df-pr 3567 df-uni 3773 df-int 3808 df-suc 4331 df-iom 4550 df-bdc 13416 df-bj-ind 13502 |
This theorem is referenced by: (None) |
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