Theorem relsucmap 39005

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 39000	. 2 ⊢ SucMap = {⟨𝑚, 𝑛⟩ ∣ suc 𝑚 = 𝑛}
2	1	relopabi 5810	1 ⊢ Rel SucMap

Syntax hints:   = wceq 1567  Rel wrel 5667  suc csuc 6363   SucMap csucmap 38716

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-11 2198  ax-12 2219  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1103  df-tru 1570  df-fal 1580  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-rab 3424  df-v 3465  df-dif 3916  df-un 3918  df-ss 3930  df-nul 4295  df-if 4493  df-sn 4595  df-pr 4597  df-op 4601  df-opab 5178  df-xp 5668  df-rel 5669  df-sucmap 39000

This theorem is referenced by:  dfpre4  39018  presuc  39036