Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 3004 | . . 3 | |
2 | ssralv 3004 | . . . . 5 | |
3 | ssralv 3004 | . . . . . 6 | |
4 | 3 | ralimdv 2388 | . . . . 5 |
5 | 2, 4 | syld 40 | . . . 4 |
6 | 5 | ralimdv 2388 | . . 3 |
7 | 1, 6 | syld 40 | . 2 |
8 | df-po 4033 | . 2 | |
9 | df-po 4033 | . 2 | |
10 | 7, 8, 9 | 3imtr4g 194 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wral 2306 wss 2917 class class class wbr 3764 wpo 4031 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-ral 2311 df-in 2924 df-ss 2931 df-po 4033 |
This theorem is referenced by: poeq2 4037 soss 4051 |
Copyright terms: Public domain | W3C validator |