Theorem relsucmap 38834

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 38829	. 2 ⊢ SucMap = {⟨𝑚, 𝑛⟩ ∣ suc 𝑚 = 𝑛}
2	1	relopabi 5765	1 ⊢ Rel SucMap

Syntax hints:   = wceq 1547  Rel wrel 5623  suc csuc 6312   SucMap csucmap 38545

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-11 2168  ax-12 2189  ax-ext 2711

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-3an 1094  df-tru 1550  df-fal 1560  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-rab 3392  df-v 3433  df-dif 3886  df-un 3888  df-ss 3900  df-nul 4262  df-if 4455  df-sn 4556  df-pr 4558  df-op 4562  df-opab 5135  df-xp 5624  df-rel 5625  df-sucmap 38829

This theorem is referenced by:  dfpre4  38847  presuc  38865