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Theorem ordsuccl 25102
Description: If a successor of  A belongs to an ordinal, so does  A. (Contributed by FL, 20-Mar-2011.)
Assertion
Ref Expression
ordsuccl  |-  ( ( Ord  B  /\  suc  A  e.  B )  ->  A  e.  B )

Proof of Theorem ordsuccl
StepHypRef Expression
1 ordtr 4406 . 2  |-  ( Ord 
B  ->  Tr  B
)
2 trsuc 4476 . 2  |-  ( ( Tr  B  /\  suc  A  e.  B )  ->  A  e.  B )
31, 2sylan 457 1  |-  ( ( Ord  B  /\  suc  A  e.  B )  ->  A  e.  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    e. wcel 1684   Tr wtr 4113   Ord word 4391   suc csuc 4394
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157  df-in 3159  df-ss 3166  df-sn 3646  df-uni 3828  df-tr 4114  df-ord 4395  df-suc 4398
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