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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdop | Unicode version |
Description: The ordered pair of two setvars is a bounded class. (Contributed by BJ, 21-Nov-2019.) |
Ref | Expression |
---|---|
bdop |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdvsn 13243 |
. . . 4
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2 | bdcpr 13240 |
. . . . . . 7
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3 | 2 | bdss 13233 |
. . . . . 6
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4 | ax-bdel 13190 |
. . . . . . . 8
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5 | ax-bdel 13190 |
. . . . . . . 8
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6 | 4, 5 | ax-bdan 13184 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | vex 2692 |
. . . . . . . . . . 11
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8 | 7 | prid1 3637 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | ssel 3096 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 8, 9 | mpi 15 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | vex 2692 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() | |
12 | 11 | prid2 3638 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | ssel 3096 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
14 | 12, 13 | mpi 15 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 10, 14 | jca 304 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | prssi 3686 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | 15, 16 | impbii 125 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 6, 17 | bd0r 13194 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 3, 18 | ax-bdan 13184 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | eqss 3117 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | 19, 20 | bd0r 13194 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 1, 21 | ax-bdor 13185 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | vex 2692 |
. . . 4
![]() ![]() ![]() ![]() | |
24 | 23, 7, 11 | elop 4161 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 22, 24 | bd0r 13194 |
. 2
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26 | 25 | bdelir 13216 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-bd0 13182 ax-bdan 13184 ax-bdor 13185 ax-bdal 13187 ax-bdeq 13189 ax-bdel 13190 ax-bdsb 13191 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-sn 3538 df-pr 3539 df-op 3541 df-bdc 13210 |
This theorem is referenced by: (None) |
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