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Mirrors > Home > ILE Home > Th. List > poss | Unicode version |
Description: Subset theorem for the partial ordering predicate. (Contributed by NM, 27-Mar-1997.) (Proof shortened by Mario Carneiro, 18-Nov-2016.) |
Ref | Expression |
---|---|
poss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssralv 3166 | . . 3 | |
2 | ssralv 3166 | . . . . 5 | |
3 | ssralv 3166 | . . . . . 6 | |
4 | 3 | ralimdv 2503 | . . . . 5 |
5 | 2, 4 | syld 45 | . . . 4 |
6 | 5 | ralimdv 2503 | . . 3 |
7 | 1, 6 | syld 45 | . 2 |
8 | df-po 4226 | . 2 | |
9 | df-po 4226 | . 2 | |
10 | 7, 8, 9 | 3imtr4g 204 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wral 2417 wss 3076 class class class wbr 3937 wpo 4224 |
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-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-ral 2422 df-in 3082 df-ss 3089 df-po 4226 |
This theorem is referenced by: poeq2 4230 soss 4244 fimaxq 10605 |
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