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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-zfpair2 | Unicode version |
Description: Proof of zfpair2 4210 using only bounded separation. (Contributed by BJ, 5-Oct-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-zfpair2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-bdeq 14508 |
. . . . 5
![]() ![]() ![]() ![]() | |
2 | ax-bdeq 14508 |
. . . . 5
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3 | 1, 2 | ax-bdor 14504 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | ax-pr 4209 |
. . . 4
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5 | 3, 4 | bdbm1.3ii 14579 |
. . 3
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6 | dfcleq 2171 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | vex 2740 |
. . . . . . . 8
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8 | 7 | elpr 3613 |
. . . . . . 7
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9 | 8 | bibi2i 227 |
. . . . . 6
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10 | 9 | albii 1470 |
. . . . 5
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11 | 6, 10 | bitri 184 |
. . . 4
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12 | 11 | exbii 1605 |
. . 3
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13 | 5, 12 | mpbir 146 |
. 2
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14 | 13 | issetri 2746 |
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-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-14 2151 ax-ext 2159 ax-pr 4209 ax-bdor 14504 ax-bdeq 14508 ax-bdsep 14572 |
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-v 2739 df-un 3133 df-sn 3598 df-pr 3599 |
This theorem is referenced by: bj-prexg 14599 |
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