Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ssuni | Unicode version |
Description: Subclass relationship for class union. (Contributed by NM, 24-May-1994.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
ssuni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq2 2239 | . . . . . . 7 | |
2 | 1 | imbi1d 231 | . . . . . 6 |
3 | elunii 3810 | . . . . . . 7 | |
4 | 3 | expcom 116 | . . . . . 6 |
5 | 2, 4 | vtoclga 2801 | . . . . 5 |
6 | 5 | imim2d 54 | . . . 4 |
7 | 6 | alimdv 1877 | . . 3 |
8 | dfss2 3142 | . . 3 | |
9 | dfss2 3142 | . . 3 | |
10 | 7, 8, 9 | 3imtr4g 205 | . 2 |
11 | 10 | impcom 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 104 wal 1351 wceq 1353 wcel 2146 wss 3127 cuni 3805 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1445 ax-7 1446 ax-gen 1447 ax-ie1 1491 ax-ie2 1492 ax-8 1502 ax-10 1503 ax-11 1504 ax-i12 1505 ax-bndl 1507 ax-4 1508 ax-17 1524 ax-i9 1528 ax-ial 1532 ax-i5r 1533 ax-ext 2157 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1459 df-sb 1761 df-clab 2162 df-cleq 2168 df-clel 2171 df-nfc 2306 df-v 2737 df-in 3133 df-ss 3140 df-uni 3806 |
This theorem is referenced by: elssuni 3833 uniss2 3836 ssorduni 4480 |
Copyright terms: Public domain | W3C validator |