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Mirrors > Home > ILE Home > Th. List > iinxprg | Unicode version |
Description: Indexed intersection with an unordered pair index. (Contributed by NM, 25-Jan-2012.) |
Ref | Expression |
---|---|
iinxprg.1 | |
iinxprg.2 |
Ref | Expression |
---|---|
iinxprg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iinxprg.1 | . . . . 5 | |
2 | 1 | eleq2d 2107 | . . . 4 |
3 | iinxprg.2 | . . . . 5 | |
4 | 3 | eleq2d 2107 | . . . 4 |
5 | 2, 4 | ralprg 3421 | . . 3 |
6 | 5 | abbidv 2155 | . 2 |
7 | df-iin 3660 | . 2 | |
8 | df-in 2924 | . 2 | |
9 | 6, 7, 8 | 3eqtr4g 2097 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wceq 1243 wcel 1393 cab 2026 wral 2306 cin 2916 cpr 3376 ciin 3658 |
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-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-v 2559 df-sbc 2765 df-un 2922 df-in 2924 df-sn 3381 df-pr 3382 df-iin 3660 |
This theorem is referenced by: (None) |
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