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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 2228 | . . . . . . 7 | |
2 | 1 | imbi1d 230 | . . . . . 6 |
3 | elunii 3789 | . . . . . . 7 | |
4 | 3 | expcom 115 | . . . . . 6 |
5 | 2, 4 | vtoclga 2788 | . . . . 5 |
6 | 5 | imim2d 54 | . . . 4 |
7 | 6 | alimdv 1866 | . . 3 |
8 | dfss2 3127 | . . 3 | |
9 | dfss2 3127 | . . 3 | |
10 | 7, 8, 9 | 3imtr4g 204 | . 2 |
11 | 10 | impcom 124 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1340 wceq 1342 wcel 2135 wss 3112 cuni 3784 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2724 df-in 3118 df-ss 3125 df-uni 3785 |
This theorem is referenced by: elssuni 3812 uniss2 3815 ssorduni 4459 |
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