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Mirrors > Home > MPE Home > Th. List > poss | Structured version Visualization version 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 3666 | . . 3 | |
2 | ssralv 3666 | . . . . 5 | |
3 | ssralv 3666 | . . . . . 6 | |
4 | 3 | ralimdv 2963 | . . . . 5 |
5 | 2, 4 | syld 47 | . . . 4 |
6 | 5 | ralimdv 2963 | . . 3 |
7 | 1, 6 | syld 47 | . 2 |
8 | df-po 5035 | . 2 | |
9 | df-po 5035 | . 2 | |
10 | 7, 8, 9 | 3imtr4g 285 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wa 384 wral 2912 wss 3574 class class class wbr 4653 wpo 5033 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-ral 2917 df-in 3581 df-ss 3588 df-po 5035 |
This theorem is referenced by: poeq2 5039 soss 5053 swoso 7775 frfi 8205 wemapsolem 8455 fin23lem27 9150 zorn2lem6 9323 xrge0iifiso 29981 incsequz2 33545 |
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