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Mirrors > Home > ILE Home > Th. List > Mathboxes > peano5set | Unicode version |
Description: Version of peano5 4598 when ![]() ![]() ![]() |
Ref | Expression |
---|---|
peano5set |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-omind 14689 |
. . . . 5
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2 | bj-indind 14687 |
. . . . 5
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3 | 1, 2 | mpan 424 |
. . . 4
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4 | bj-omssind 14690 |
. . . . 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 3357 |
. . 3
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8 | 6, 7 | sstrdi 3168 |
. 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 4130 ax-pr 4210 ax-un 4434 ax-bd0 14568 ax-bdor 14571 ax-bdex 14574 ax-bdeq 14575 ax-bdel 14576 ax-bdsb 14577 ax-bdsep 14639 |
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 2740 df-dif 3132 df-un 3134 df-in 3136 df-ss 3143 df-nul 3424 df-sn 3599 df-pr 3600 df-uni 3811 df-int 3846 df-suc 4372 df-iom 4591 df-bdc 14596 df-bj-ind 14682 |
This theorem is referenced by: bdpeano5 14698 speano5 14699 |
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