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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 1457 | . . . 4 | |
2 | vex 2684 | . . . . . . . 8 | |
3 | 2 | elpr 3543 | . . . . . . 7 |
4 | 3 | imbi1i 237 | . . . . . 6 |
5 | jaob 699 | . . . . . 6 | |
6 | 4, 5 | bitri 183 | . . . . 5 |
7 | 6 | albii 1446 | . . . 4 |
8 | intpr.1 | . . . . . 6 | |
9 | 8 | clel4 2816 | . . . . 5 |
10 | intpr.2 | . . . . . 6 | |
11 | 10 | clel4 2816 | . . . . 5 |
12 | 9, 11 | anbi12i 455 | . . . 4 |
13 | 1, 7, 12 | 3bitr4i 211 | . . 3 |
14 | vex 2684 | . . . 4 | |
15 | 14 | elint 3772 | . . 3 |
16 | elin 3254 | . . 3 | |
17 | 13, 15, 16 | 3bitr4i 211 | . 2 |
18 | 17 | eqriv 2134 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wo 697 wal 1329 wceq 1331 wcel 1480 cvv 2681 cin 3065 cpr 3523 cint 3766 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-in 3072 df-sn 3528 df-pr 3529 df-int 3767 |
This theorem is referenced by: intprg 3799 op1stb 4394 onintexmid 4482 |
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