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Mirrors > Home > ILE Home > Th. List > eldifpr | Unicode version |
Description: Membership in a set with two elements removed. Similar to eldifsn 3687 and eldiftp 3606. (Contributed by Mario Carneiro, 18-Jul-2017.) |
Ref | Expression |
---|---|
eldifpr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elprg 3580 | . . . . 5 | |
2 | 1 | notbid 657 | . . . 4 |
3 | neanior 2414 | . . . 4 | |
4 | 2, 3 | bitr4di 197 | . . 3 |
5 | 4 | pm5.32i 450 | . 2 |
6 | eldif 3111 | . 2 | |
7 | 3anass 967 | . 2 | |
8 | 5, 6, 7 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wb 104 wo 698 w3a 963 wceq 1335 wcel 2128 wne 2327 cdif 3099 cpr 3561 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-v 2714 df-dif 3104 df-un 3106 df-sn 3566 df-pr 3567 |
This theorem is referenced by: rexdifpr 3588 rplogbval 13304 |
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