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Theorem bnj219 29077
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 2804 . . 3  |-  m  e. 
_V
21bnj216 29076 . 2  |-  ( n  =  suc  m  ->  m  e.  n )
3 epel 4324 . 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 1632    e. wcel 1696   class class class wbr 4039    _E cep 4319   suc csuc 4410
This theorem is referenced by:  bnj605  29255  bnj594  29260  bnj607  29264  bnj1110  29328
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-eprel 4321  df-suc 4414
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