Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > inopab | Unicode version |
Description: Intersection of two ordered pair class abstractions. (Contributed by NM, 30-Sep-2002.) |
Ref | Expression |
---|---|
inopab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relopab 4464 | . . 3 | |
2 | relin1 4455 | . . 3 | |
3 | 1, 2 | ax-mp 7 | . 2 |
4 | relopab 4464 | . 2 | |
5 | sban 1829 | . . . 4 | |
6 | sban 1829 | . . . . 5 | |
7 | 6 | sbbii 1648 | . . . 4 |
8 | opelopabsbALT 3996 | . . . . 5 | |
9 | opelopabsbALT 3996 | . . . . 5 | |
10 | 8, 9 | anbi12i 433 | . . . 4 |
11 | 5, 7, 10 | 3bitr4ri 202 | . . 3 |
12 | elin 3126 | . . 3 | |
13 | opelopabsbALT 3996 | . . 3 | |
14 | 11, 12, 13 | 3bitr4i 201 | . 2 |
15 | 3, 4, 14 | eqrelriiv 4434 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wceq 1243 wcel 1393 wsb 1645 cin 2916 cop 3378 copab 3817 wrel 4350 |
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 df-rel 4352 |
This theorem is referenced by: inxp 4470 resopab 4652 cnvin 4731 fndmin 5274 enq0enq 6529 |
Copyright terms: Public domain | W3C validator |