Theorem relsucmap 38788

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 38783	. 2 ⊢ SucMap = {⟨𝑚, 𝑛⟩ ∣ suc 𝑚 = 𝑛}
2	1	relopabi 5778	1 ⊢ Rel SucMap

Syntax hints:   = wceq 1542  Rel wrel 5636  suc csuc 6325   SucMap csucmap 38499

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-11 2163  ax-12 2185  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-rab 3390  df-v 3431  df-dif 3892  df-un 3894  df-ss 3906  df-nul 4274  df-if 4467  df-sn 4568  df-pr 4570  df-op 4574  df-opab 5148  df-xp 5637  df-rel 5638  df-sucmap 38783

This theorem is referenced by:  dfpre4  38801  presuc  38819