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Mirrors > Home > ILE Home > Th. List > uniss | Unicode version |
Description: Subclass relationship for class union. Theorem 61 of [Suppes] p. 39. (Contributed by NM, 22-Mar-1998.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
uniss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3134 | . . . . 5 | |
2 | 1 | anim2d 335 | . . . 4 |
3 | 2 | eximdv 1867 | . . 3 |
4 | eluni 3789 | . . 3 | |
5 | eluni 3789 | . . 3 | |
6 | 3, 4, 5 | 3imtr4g 204 | . 2 |
7 | 6 | ssrdv 3146 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wex 1479 wcel 2135 wss 3114 cuni 3786 |
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 2726 df-in 3120 df-ss 3127 df-uni 3787 |
This theorem is referenced by: unissi 3809 unissd 3810 intssuni2m 3845 relfld 5129 tgcl 12662 distop 12683 |
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