Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj551 Structured version   Visualization version   GIF version

Theorem bnj551 34373
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 𝑝𝑚 = suc 𝑖) → 𝑝 = 𝑖)

Proof of Theorem bnj551
StepHypRef Expression
1 eqtr2 2752 . 2 ((𝑚 = suc 𝑝𝑚 = suc 𝑖) → suc 𝑝 = suc 𝑖)
2 suc11reg 9643 . 2 (suc 𝑝 = suc 𝑖𝑝 = 𝑖)
31, 2sylib 217 1 ((𝑚 = suc 𝑝𝑚 = suc 𝑖) → 𝑝 = 𝑖)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395   = wceq 1534  suc csuc 6371
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-12 2167  ax-ext 2699  ax-sep 5299  ax-nul 5306  ax-pr 5429  ax-un 7740  ax-reg 9616
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-nf 1779  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-ne 2938  df-ral 3059  df-rex 3068  df-rab 3430  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4324  df-if 4530  df-pw 4605  df-sn 4630  df-pr 4632  df-op 4636  df-uni 4909  df-br 5149  df-opab 5211  df-eprel 5582  df-fr 5633  df-suc 6375
This theorem is referenced by:  bnj554  34530  bnj557  34532  bnj966  34575
  Copyright terms: Public domain W3C validator