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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 13976 (see bj-2inf 13973 for the equivalence of the latter with bj-omex 13977). (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 14011 | . . 3 | |
2 | vex 2733 | . . . 4 | |
3 | bdcv 13883 | . . . . 5 BOUNDED | |
4 | 3 | bj-inf2vn 14009 | . . . 4 |
5 | 2, 4 | ax-mp 5 | . . 3 |
6 | 1, 5 | eximii 1595 | . 2 |
7 | 6 | issetri 2739 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wo 703 wal 1346 wceq 1348 wcel 2141 wrex 2449 cvv 2730 c0 3414 csuc 4350 com 4574 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-nul 4115 ax-pr 4194 ax-un 4418 ax-bd0 13848 ax-bdim 13849 ax-bdor 13851 ax-bdex 13854 ax-bdeq 13855 ax-bdel 13856 ax-bdsb 13857 ax-bdsep 13919 ax-bdsetind 14003 ax-inf2 14011 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-rab 2457 df-v 2732 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-nul 3415 df-sn 3589 df-pr 3590 df-uni 3797 df-int 3832 df-suc 4356 df-iom 4575 df-bdc 13876 df-bj-ind 13962 |
This theorem is referenced by: (None) |
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