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Mirrors > Home > ILE Home > Th. List > intpr | Unicode version |
Description: The intersection of a pair is the intersection of its members. Theorem 71 of [Suppes] p. 42. (Contributed by NM, 14-Oct-1999.) |
Ref | Expression |
---|---|
intpr.1 | |
intpr.2 |
Ref | Expression |
---|---|
intpr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.26 1370 | . . . 4 | |
2 | vex 2560 | . . . . . . . 8 | |
3 | 2 | elpr 3396 | . . . . . . 7 |
4 | 3 | imbi1i 227 | . . . . . 6 |
5 | jaob 631 | . . . . . 6 | |
6 | 4, 5 | bitri 173 | . . . . 5 |
7 | 6 | albii 1359 | . . . 4 |
8 | intpr.1 | . . . . . 6 | |
9 | 8 | clel4 2680 | . . . . 5 |
10 | intpr.2 | . . . . . 6 | |
11 | 10 | clel4 2680 | . . . . 5 |
12 | 9, 11 | anbi12i 433 | . . . 4 |
13 | 1, 7, 12 | 3bitr4i 201 | . . 3 |
14 | vex 2560 | . . . 4 | |
15 | 14 | elint 3621 | . . 3 |
16 | elin 3126 | . . 3 | |
17 | 13, 15, 16 | 3bitr4i 201 | . 2 |
18 | 17 | eqriv 2037 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wo 629 wal 1241 wceq 1243 wcel 1393 cvv 2557 cin 2916 cpr 3376 cint 3615 |
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-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 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-sn 3381 df-pr 3382 df-int 3616 |
This theorem is referenced by: intprg 3648 op1stb 4209 onintexmid 4297 |
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