Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 3217 | . . . . 5 | |
4 | 3 | bibi1i 227 | . . . 4 |
5 | 1, 2, 4 | 3bitr4i 211 | . . 3 |
6 | 5 | albii 1446 | . 2 |
7 | dfss2 3086 | . 2 | |
8 | dfcleq 2133 | . 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 3069 wss 3071 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 |
This theorem is referenced by: ssequn2 3249 uniop 4177 pwssunim 4206 unisuc 4335 unisucg 4336 rdgisucinc 6282 oasuc 6360 omsuc 6368 undifdc 6812 |
Copyright terms: Public domain | W3C validator |