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Mirrors > Home > ILE Home > Th. List > onntri24 | Unicode version |
Description: Double negated ordinal trichotomy. (Contributed by James E. Hanson and Jim Kingdon, 2-Aug-2024.) |
Ref | Expression |
---|---|
onntri24 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnral 2460 | . 2 | |
2 | nnral 2460 | . . 3 | |
3 | 2 | ralimi 2533 | . 2 |
4 | 1, 3 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wo 703 wral 2448 wss 3121 con0 4348 |
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-in1 609 ax-in2 610 ax-5 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-4 1503 ax-17 1519 ax-ial 1527 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-fal 1354 df-nf 1454 df-ral 2453 df-rex 2454 |
This theorem is referenced by: onntri2or 7223 |
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