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Mirrors > Home > ILE Home > Th. List > intprg | Unicode version |
Description: The intersection of a pair is the intersection of its members. Closed form of intpr 3647. Theorem 71 of [Suppes] p. 42. (Contributed by FL, 27-Apr-2008.) |
Ref | Expression |
---|---|
intprg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | preq1 3447 | . . . 4 | |
2 | 1 | inteqd 3620 | . . 3 |
3 | ineq1 3131 | . . 3 | |
4 | 2, 3 | eqeq12d 2054 | . 2 |
5 | preq2 3448 | . . . 4 | |
6 | 5 | inteqd 3620 | . . 3 |
7 | ineq2 3132 | . . 3 | |
8 | 6, 7 | eqeq12d 2054 | . 2 |
9 | vex 2560 | . . 3 | |
10 | vex 2560 | . . 3 | |
11 | 9, 10 | intpr 3647 | . 2 |
12 | 4, 8, 11 | vtocl2g 2617 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wceq 1243 wcel 1393 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-ral 2311 df-v 2559 df-un 2922 df-in 2924 df-sn 3381 df-pr 3382 df-int 3616 |
This theorem is referenced by: intsng 3649 op1stbg 4210 |
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