Theorem relsucmap 39536

Description: The successor map is a relation. (Contributed by Peter Mazsa, 7-Jan-2026.)

Assertion

Ref	Expression
relsucmap	⊢ Rel SucMap

Proof of Theorem relsucmap

Dummy variables 𝑚 𝑛 are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-sucmap 39531	. 2 ⊢ SucMap = {⟨𝑚, 𝑛⟩ ∣ suc 𝑚 = 𝑛}
2	1	relopabi 5801	1 ⊢ Rel SucMap

This proof depends on syntax axioms:   = wceq 1569  Rel wrel 5656  suc csuc 6367   SucMap csucmap 39247

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-11 2193  ax-12 2212  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-rab 3413  df-v 3452  df-ss 3897  df-dif 4046  df-un 4150  df-nul 4278  df-if 4482  df-sn 4585  df-pr 4587  df-op 4835  df-opab 5167  df-xp 5657  df-rel 5658  df-sucmap 39531

This theorem is used by:  dfpre4  39549  presuc  39567