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Mirrors > Home > ILE Home > Th. List > eltp | Unicode version |
Description: A member of an unordered triple of classes is one of them. Special case of Exercise 1 of [TakeutiZaring] p. 17. (Contributed by NM, 8-Apr-1994.) (Revised by Mario Carneiro, 11-Feb-2015.) |
Ref | Expression |
---|---|
eltp.1 |
Ref | Expression |
---|---|
eltp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eltp.1 | . 2 | |
2 | eltpg 3605 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 w3o 962 wceq 1335 wcel 2128 cvv 2712 ctp 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-3or 964 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 3566 df-pr 3567 df-tp 3568 |
This theorem is referenced by: dftp2 3609 tpid1 3671 tpid2 3673 tpid3 3676 |
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