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Mirrors > Home > ILE Home > Th. List > iineq2 | Unicode version |
Description: Equality theorem for indexed intersection. (Contributed by NM, 22-Oct-2003.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
iineq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq2 2101 | . . . . 5 | |
2 | 1 | ralimi 2384 | . . . 4 |
3 | ralbi 2445 | . . . 4 | |
4 | 2, 3 | syl 14 | . . 3 |
5 | 4 | abbidv 2155 | . 2 |
6 | df-iin 3660 | . 2 | |
7 | df-iin 3660 | . 2 | |
8 | 5, 6, 7 | 3eqtr4g 2097 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wceq 1243 wcel 1393 cab 2026 wral 2306 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-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 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-ral 2311 df-iin 3660 |
This theorem is referenced by: iineq2i 3676 iineq2d 3677 |
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