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Mirrors > Home > ILE Home > Th. List > ispod | Unicode version |
Description: Sufficient conditions for a partial order. (Contributed by NM, 9-Jul-2014.) |
Ref | Expression |
---|---|
ispod.1 |
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ispod.2 |
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Ref | Expression |
---|---|
ispod |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ispod.1 |
. . . . 5
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2 | 1 | 3ad2antr1 1147 |
. . . 4
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3 | ispod.2 |
. . . 4
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4 | 2, 3 | jca 304 |
. . 3
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5 | 4 | ralrimivvva 2518 |
. 2
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6 | df-po 4226 |
. 2
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7 | 5, 6 | sylibr 133 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-gen 1426 ax-4 1488 ax-17 1507 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-nf 1438 df-ral 2422 df-po 4226 |
This theorem is referenced by: swopo 4236 pofun 4242 wepo 4289 ltsopi 7152 ltsonq 7230 ltpopr 7427 ltposr 7595 ltso 7866 xrltso 9612 |
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