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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 1069 | . . . 4 |
3 | ispod.2 | . . . 4 | |
4 | 2, 3 | jca 290 | . . 3 |
5 | 4 | ralrimivvva 2402 | . 2 |
6 | df-po 4033 | . 2 | |
7 | 5, 6 | sylibr 137 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 w3a 885 wcel 1393 wral 2306 class class class wbr 3764 wpo 4031 |
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-gen 1338 ax-4 1400 ax-17 1419 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-nf 1350 df-ral 2311 df-po 4033 |
This theorem is referenced by: swopo 4043 pofun 4049 wepo 4096 ltsopi 6418 ltsonq 6496 ltpopr 6693 ltposr 6848 ltso 7096 xrltso 8717 |
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