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Theorem bnj219 29370
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 3081 . . 3  |-  m  e. 
_V
21bnj216 29369 . 2  |-  ( n  =  suc  m  ->  m  e.  n )
3 epel 4759 . 2  |-  ( m  _E  n  <->  m  e.  n )
42, 3sylibr 215 1  |-  ( n  =  suc  m  ->  m  _E  n )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1437   class class class wbr 4417    _E cep 4754   suc csuc 5435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-9 1871  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398  ax-sep 4539  ax-nul 4547  ax-pr 4652
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-eu 2267  df-mo 2268  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ne 2618  df-rab 2782  df-v 3080  df-dif 3436  df-un 3438  df-in 3440  df-ss 3447  df-nul 3759  df-if 3907  df-sn 3994  df-pr 3996  df-op 4000  df-br 4418  df-opab 4476  df-eprel 4756  df-suc 5439
This theorem is referenced by:  bnj605  29547  bnj594  29552  bnj607  29556  bnj1110  29620
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