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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 | |
ispod.2 |
Ref | Expression |
---|---|
ispod |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ispod.1 | . . . . 5 | |
2 | 1 | 3ad2antr1 1157 | . . . 4 |
3 | ispod.2 | . . . 4 | |
4 | 2, 3 | jca 304 | . . 3 |
5 | 4 | ralrimivvva 2553 | . 2 |
6 | df-po 4281 | . 2 | |
7 | 5, 6 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 w3a 973 wcel 2141 wral 2448 class class class wbr 3989 wpo 4279 |
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 1440 ax-gen 1442 ax-4 1503 ax-17 1519 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-nf 1454 df-ral 2453 df-po 4281 |
This theorem is referenced by: swopo 4291 pofun 4297 wepo 4344 ltsopi 7282 ltsonq 7360 ltpopr 7557 ltposr 7725 ltso 7997 xrltso 9753 |
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