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Theorem ordelss 4082
Description: An element of an ordinal class is a subset of it. (Contributed by NM, 30-May-1994.)
Assertion
Ref Expression
ordelss ((Ord A B A) → BA)

Proof of Theorem ordelss
StepHypRef Expression
1 ordtr 4081 . 2 (Ord A → Tr A)
2 trss 3854 . . 3 (Tr A → (B ABA))
32imp 115 . 2 ((Tr A B A) → BA)
41, 3sylan 267 1 ((Ord A B A) → BA)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   wcel 1390  wss 2911  Tr wtr 3845  Ord word 4065
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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-v 2553  df-in 2918  df-ss 2925  df-uni 3572  df-tr 3846  df-iord 4069
This theorem is referenced by:  ordelord  4084  onelss  4090  ordsuc  4241  smores3  5849  tfrlem1  5864  tfrlemisucaccv  5880  tfrlemiubacc  5885  nntri1  6013
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