Theorem relsucmap 38919

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 38914	. 2 ⊢ SucMap = {⟨𝑚, 𝑛⟩ ∣ suc 𝑚 = 𝑛}
2	1	relopabi 5793	1 ⊢ Rel SucMap

Syntax hints:   = wceq 1559  Rel wrel 5650  suc csuc 6342   SucMap csucmap 38630

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-11 2190  ax-12 2211  ax-ext 2733

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-3an 1099  df-tru 1562  df-fal 1572  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-rab 3414  df-v 3455  df-dif 3907  df-un 3909  df-ss 3921  df-nul 4286  df-if 4480  df-sn 4582  df-pr 4584  df-op 4588  df-opab 5162  df-xp 5651  df-rel 5652  df-sucmap 38914

This theorem is referenced by:  dfpre4  38932  presuc  38950