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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssralv 3004 |
. . 3
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2 | ssralv 3004 |
. . . . 5
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3 | ssralv 3004 |
. . . . . 6
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4 | 3 | ralimdv 2388 |
. . . . 5
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5 | 2, 4 | syld 40 |
. . . 4
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6 | 5 | ralimdv 2388 |
. . 3
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7 | 1, 6 | syld 40 |
. 2
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8 | df-po 4033 |
. 2
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9 | df-po 4033 |
. 2
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10 | 7, 8, 9 | 3imtr4g 194 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
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 |
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