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Theorem bnj551 28771
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj551  |-  ( ( m  =  suc  p  /\  m  =  suc  i )  ->  p  =  i )

Proof of Theorem bnj551
StepHypRef Expression
1 eqtr2 2301 . 2  |-  ( ( m  =  suc  p  /\  m  =  suc  i )  ->  suc  p  =  suc  i )
2 suc11reg 7320 . 2  |-  ( suc  p  =  suc  i  <->  p  =  i )
31, 2sylib 188 1  |-  ( ( m  =  suc  p  /\  m  =  suc  i )  ->  p  =  i )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    = wceq 1623   suc csuc 4394
This theorem is referenced by:  bnj554  28931  bnj557  28933  bnj966  28976
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-13 1686  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  ax-un 4512  ax-reg 7306
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-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  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-uni 3828  df-br 4024  df-opab 4078  df-eprel 4305  df-fr 4352  df-suc 4398
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