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Mirrors > Home > ILE Home > Th. List > ordtr | GIF version |
Description: An ordinal class is transitive. (Contributed by NM, 3-Apr-1994.) |
Ref | Expression |
---|---|
ordtr | ⊢ (Ord A → Tr A) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dford3 4070 | . 2 ⊢ (Ord A ↔ (Tr A ∧ ∀x ∈ A Tr x)) | |
2 | 1 | simplbi 259 | 1 ⊢ (Ord A → Tr A) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wral 2300 Tr wtr 3845 Ord word 4065 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 |
This theorem depends on definitions: df-bi 110 df-iord 4069 |
This theorem is referenced by: ordelss 4082 ordin 4088 ordtr1 4091 orduniss 4128 ontrci 4130 ordon 4178 ordsucim 4192 ordsucss 4196 onsucsssucr 4200 ordsucunielexmid 4216 nlimsucg 4242 ordpwsucss 4243 tfrexlem 5889 |
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