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Mirrors > Home > ILE Home > Th. List > dmtpop | Unicode version |
Description: The domain of an unordered triple of ordered pairs. (Contributed by NM, 14-Sep-2011.) |
Ref | Expression |
---|---|
dmsnop.1 | |
dmprop.1 | |
dmtpop.1 |
Ref | Expression |
---|---|
dmtpop |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-tp 3383 | . . . 4 | |
2 | 1 | dmeqi 4536 | . . 3 |
3 | dmun 4542 | . . 3 | |
4 | dmsnop.1 | . . . . 5 | |
5 | dmprop.1 | . . . . 5 | |
6 | 4, 5 | dmprop 4795 | . . . 4 |
7 | dmtpop.1 | . . . . 5 | |
8 | 7 | dmsnop 4794 | . . . 4 |
9 | 6, 8 | uneq12i 3095 | . . 3 |
10 | 2, 3, 9 | 3eqtri 2064 | . 2 |
11 | df-tp 3383 | . 2 | |
12 | 10, 11 | eqtr4i 2063 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1243 wcel 1393 cvv 2557 cun 2915 csn 3375 cpr 3376 ctp 3377 cop 3378 cdm 4345 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-tp 3383 df-op 3384 df-br 3765 df-dm 4355 |
This theorem is referenced by: fntp 4956 |
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