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Theorem bnj219 29037
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 2951 . . 3  |-  m  e. 
_V
21bnj216 29036 . 2  |-  ( n  =  suc  m  ->  m  e.  n )
3 epel 4489 . 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 1652   class class class wbr 4204    _E cep 4484   suc csuc 4575
This theorem is referenced by:  bnj605  29215  bnj594  29220  bnj607  29224  bnj1110  29288
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-eprel 4486  df-suc 4579
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