Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > unimax | Unicode version |
Description: Any member of a class is the largest of those members that it includes. (Contributed by NM, 13-Aug-2002.) |
Ref | Expression |
---|---|
unimax |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssid 3158 | . . 3 | |
2 | sseq1 3161 | . . . 4 | |
3 | 2 | elrab3 2879 | . . 3 |
4 | 1, 3 | mpbiri 167 | . 2 |
5 | sseq1 3161 | . . . . 5 | |
6 | 5 | elrab 2878 | . . . 4 |
7 | 6 | simprbi 273 | . . 3 |
8 | 7 | rgen 2517 | . 2 |
9 | ssunieq 3817 | . . 3 | |
10 | 9 | eqcomd 2170 | . 2 |
11 | 4, 8, 10 | sylancl 410 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 wcel 2135 wral 2442 crab 2446 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-ral 2447 df-rab 2451 df-v 2724 df-in 3118 df-ss 3125 df-uni 3785 |
This theorem is referenced by: onuniss2 4484 |
Copyright terms: Public domain | W3C validator |