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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 1103 | . . . 4 |
3 | ispod.2 | . . . 4 | |
4 | 2, 3 | jca 300 | . . 3 |
5 | 4 | ralrimivvva 2444 | . 2 |
6 | df-po 4051 | . 2 | |
7 | 5, 6 | sylibr 132 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 w3a 919 wcel 1433 wral 2348 class class class wbr 3785 wpo 4049 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-4 1440 ax-17 1459 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-nf 1390 df-ral 2353 df-po 4051 |
This theorem is referenced by: swopo 4061 pofun 4067 wepo 4114 ltsopi 6510 ltsonq 6588 ltpopr 6785 ltposr 6940 ltso 7189 xrltso 8871 |
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