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Mirrors > Home > ILE Home > Th. List > opelvv | Unicode version |
Description: Ordered pair membership in the universal class of ordered pairs. (Contributed by NM, 22-Aug-2013.) (Revised by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
opelvv.1 | |
opelvv.2 |
Ref | Expression |
---|---|
opelvv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelvv.1 | . 2 | |
2 | opelvv.2 | . 2 | |
3 | opelxpi 4376 | . 2 | |
4 | 1, 2, 3 | mp2an 402 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1393 cvv 2557 cop 3378 cxp 4343 |
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-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-opab 3819 df-xp 4351 |
This theorem is referenced by: relsnop 4444 relopabi 4463 eqop2 5804 |
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