Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > iinuniss | Unicode version |
Description: A relationship involving union and indexed intersection. Exercise 23 of [Enderton] p. 33 but with equality changed to subset. (Contributed by Jim Kingdon, 19-Aug-2018.) |
Ref | Expression |
---|---|
iinuniss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.32vr 2458 | . . . 4 | |
2 | vex 2560 | . . . . . 6 | |
3 | 2 | elint2 3622 | . . . . 5 |
4 | 3 | orbi2i 679 | . . . 4 |
5 | elun 3084 | . . . . 5 | |
6 | 5 | ralbii 2330 | . . . 4 |
7 | 1, 4, 6 | 3imtr4i 190 | . . 3 |
8 | 7 | ss2abi 3012 | . 2 |
9 | df-un 2922 | . 2 | |
10 | df-iin 3660 | . 2 | |
11 | 8, 9, 10 | 3sstr4i 2984 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 629 wcel 1393 cab 2026 wral 2306 cun 2915 wss 2917 cint 3615 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-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-ss 2931 df-int 3616 df-iin 3660 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |