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Theorem bnj219 28761
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj219  |-  ( n  =  suc  m  ->  m  _E  n )

Proof of Theorem bnj219
StepHypRef Expression
1 vex 2791 . . 3  |-  m  e. 
_V
21bnj216 28760 . 2  |-  ( n  =  suc  m  ->  m  e.  n )
3 epel 4308 . 2  |-  ( m  _E  n  <->  m  e.  n )
42, 3sylibr 203 1  |-  ( n  =  suc  m  ->  m  _E  n )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623    e. wcel 1684   class class class wbr 4023    _E cep 4303   suc csuc 4394
This theorem is referenced by:  bnj605  28939  bnj594  28944  bnj607  28948  bnj1110  29012
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-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-eprel 4305  df-suc 4398
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