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Mirrors > Home > ILE Home > Th. List > elpr2 | Unicode version |
Description: A member of an unordered pair of classes is one or the other of them. Exercise 1 of [TakeutiZaring] p. 15. (Contributed by NM, 14-Oct-2005.) |
Ref | Expression |
---|---|
elpr2.1 | |
elpr2.2 |
Ref | Expression |
---|---|
elpr2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elprg 3581 | . . 3 | |
2 | 1 | ibi 175 | . 2 |
3 | elpr2.1 | . . . . . 6 | |
4 | eleq1 2220 | . . . . . 6 | |
5 | 3, 4 | mpbiri 167 | . . . . 5 |
6 | elpr2.2 | . . . . . 6 | |
7 | eleq1 2220 | . . . . . 6 | |
8 | 6, 7 | mpbiri 167 | . . . . 5 |
9 | 5, 8 | jaoi 706 | . . . 4 |
10 | elprg 3581 | . . . 4 | |
11 | 9, 10 | syl 14 | . . 3 |
12 | 11 | ibir 176 | . 2 |
13 | 2, 12 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wo 698 wceq 1335 wcel 2128 cvv 2712 cpr 3562 |
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 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-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-sn 3567 df-pr 3568 |
This theorem is referenced by: elxr 9690 |
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