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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-zfpair2 | Unicode version |
Description: Proof of zfpair2 4102 using only bounded separation. (Contributed by BJ, 5-Oct-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-zfpair2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-bdeq 12945 | . . . . 5 BOUNDED | |
2 | ax-bdeq 12945 | . . . . 5 BOUNDED | |
3 | 1, 2 | ax-bdor 12941 | . . . 4 BOUNDED |
4 | ax-pr 4101 | . . . 4 | |
5 | 3, 4 | bdbm1.3ii 13016 | . . 3 |
6 | dfcleq 2111 | . . . . 5 | |
7 | vex 2663 | . . . . . . . 8 | |
8 | 7 | elpr 3518 | . . . . . . 7 |
9 | 8 | bibi2i 226 | . . . . . 6 |
10 | 9 | albii 1431 | . . . . 5 |
11 | 6, 10 | bitri 183 | . . . 4 |
12 | 11 | exbii 1569 | . . 3 |
13 | 5, 12 | mpbir 145 | . 2 |
14 | 13 | issetri 2669 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wo 682 wal 1314 wceq 1316 wex 1453 wcel 1465 cvv 2660 cpr 3498 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-pr 4101 ax-bdor 12941 ax-bdeq 12945 ax-bdsep 13009 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 |
This theorem is referenced by: bj-prexg 13036 |
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