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Mirrors > Home > ILE Home > Th. List > ssequn1 | Unicode version |
Description: A relationship between subclass and union. Theorem 26 of [Suppes] p. 27. (Contributed by NM, 30-Aug-1993.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
ssequn1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bicom 139 | . . . 4 | |
2 | pm4.72 812 | . . . 4 | |
3 | elun 3212 | . . . . 5 | |
4 | 3 | bibi1i 227 | . . . 4 |
5 | 1, 2, 4 | 3bitr4i 211 | . . 3 |
6 | 5 | albii 1446 | . 2 |
7 | dfss2 3081 | . 2 | |
8 | dfcleq 2131 | . 2 | |
9 | 6, 7, 8 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wo 697 wal 1329 wceq 1331 wcel 1480 cun 3064 wss 3066 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 |
This theorem is referenced by: ssequn2 3244 uniop 4172 pwssunim 4201 unisuc 4330 unisucg 4331 rdgisucinc 6275 oasuc 6353 omsuc 6361 undifdc 6805 |
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