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Mirrors > Home > ILE Home > Th. List > iinexgm | Unicode version |
Description: The existence of an indexed union. is normally a free-variable parameter in , which should be read . (Contributed by Jim Kingdon, 28-Aug-2018.) |
Ref | Expression |
---|---|
iinexgm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfiin2g 3690 | . . 3 | |
2 | 1 | adantl 262 | . 2 |
3 | elisset 2568 | . . . . . . . . . 10 | |
4 | 3 | rgenw 2376 | . . . . . . . . 9 |
5 | r19.2m 3309 | . . . . . . . . 9 | |
6 | 4, 5 | mpan2 401 | . . . . . . . 8 |
7 | r19.35-1 2460 | . . . . . . . 8 | |
8 | 6, 7 | syl 14 | . . . . . . 7 |
9 | 8 | imp 115 | . . . . . 6 |
10 | rexcom4 2577 | . . . . . 6 | |
11 | 9, 10 | sylib 127 | . . . . 5 |
12 | abid 2028 | . . . . . 6 | |
13 | 12 | exbii 1496 | . . . . 5 |
14 | 11, 13 | sylibr 137 | . . . 4 |
15 | nfv 1421 | . . . . 5 | |
16 | nfsab1 2030 | . . . . 5 | |
17 | eleq1 2100 | . . . . 5 | |
18 | 15, 16, 17 | cbvex 1639 | . . . 4 |
19 | 14, 18 | sylib 127 | . . 3 |
20 | inteximm 3903 | . . 3 | |
21 | 19, 20 | syl 14 | . 2 |
22 | 2, 21 | eqeltrd 2114 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wceq 1243 wex 1381 wcel 1393 cab 2026 wral 2306 wrex 2307 cvv 2557 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 ax-sep 3875 |
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-rex 2312 df-v 2559 df-in 2924 df-ss 2931 df-int 3616 df-iin 3660 |
This theorem is referenced by: (None) |
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