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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, ![]() |
Ref | Expression |
---|---|
bj-omex2 |
![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-inf2 14767 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | vex 2742 |
. . . 4
![]() ![]() ![]() ![]() | |
3 | bdcv 14639 |
. . . . 5
![]() ![]() | |
4 | 3 | bj-inf2vn 14765 |
. . . 4
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5 | 2, 4 | ax-mp 5 |
. . 3
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6 | 1, 5 | eximii 1602 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() |
7 | 6 | issetri 2748 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-nul 4131 ax-pr 4211 ax-un 4435 ax-bd0 14604 ax-bdim 14605 ax-bdor 14607 ax-bdex 14610 ax-bdeq 14611 ax-bdel 14612 ax-bdsb 14613 ax-bdsep 14675 ax-bdsetind 14759 ax-inf2 14767 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2741 df-dif 3133 df-un 3135 df-in 3137 df-ss 3144 df-nul 3425 df-sn 3600 df-pr 3601 df-uni 3812 df-int 3847 df-suc 4373 df-iom 4592 df-bdc 14632 df-bj-ind 14718 |
This theorem is referenced by: (None) |
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