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Mirrors > Home > ILE Home > Th. List > Mathboxes > peano5set | Unicode version |
Description: Version of peano5 4597 when ![]() ![]() ![]() |
Ref | Expression |
---|---|
peano5set |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-omind 14656 |
. . . . 5
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2 | bj-indind 14654 |
. . . . 5
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3 | 1, 2 | mpan 424 |
. . . 4
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4 | bj-omssind 14657 |
. . . . 5
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5 | 4 | imp 124 |
. . . 4
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6 | 3, 5 | sylan2 286 |
. . 3
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7 | inss2 3356 |
. . 3
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8 | 6, 7 | sstrdi 3167 |
. 2
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9 | 8 | ex 115 |
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 4129 ax-pr 4209 ax-un 4433 ax-bd0 14535 ax-bdor 14538 ax-bdex 14541 ax-bdeq 14542 ax-bdel 14543 ax-bdsb 14544 ax-bdsep 14606 |
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 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-nul 3423 df-sn 3598 df-pr 3599 df-uni 3810 df-int 3845 df-suc 4371 df-iom 4590 df-bdc 14563 df-bj-ind 14649 |
This theorem is referenced by: bdpeano5 14665 speano5 14666 |
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