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Theorem bnj219 28439
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 2903 . . 3  |-  m  e. 
_V
21bnj216 28438 . 2  |-  ( n  =  suc  m  ->  m  e.  n )
3 epel 4439 . 2  |-  ( m  _E  n  <->  m  e.  n )
42, 3sylibr 204 1  |-  ( n  =  suc  m  ->  m  _E  n )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649   class class class wbr 4154    _E cep 4434   suc csuc 4525
This theorem is referenced by:  bnj605  28617  bnj594  28622  bnj607  28626  bnj1110  28690
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369  ax-sep 4272  ax-nul 4280  ax-pr 4345
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2243  df-mo 2244  df-clab 2375  df-cleq 2381  df-clel 2384  df-nfc 2513  df-ne 2553  df-rab 2659  df-v 2902  df-dif 3267  df-un 3269  df-in 3271  df-ss 3278  df-nul 3573  df-if 3684  df-sn 3764  df-pr 3765  df-op 3767  df-br 4155  df-opab 4209  df-eprel 4436  df-suc 4529
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