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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 1147 | . . . 4 |
3 | ispod.2 | . . . 4 | |
4 | 2, 3 | jca 304 | . . 3 |
5 | 4 | ralrimivvva 2540 | . 2 |
6 | df-po 4259 | . 2 | |
7 | 5, 6 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 w3a 963 wcel 2128 wral 2435 class class class wbr 3967 wpo 4257 |
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 1427 ax-gen 1429 ax-4 1490 ax-17 1506 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-nf 1441 df-ral 2440 df-po 4259 |
This theorem is referenced by: swopo 4269 pofun 4275 wepo 4322 ltsopi 7243 ltsonq 7321 ltpopr 7518 ltposr 7686 ltso 7958 xrltso 9710 |
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