Theorem reldmlmd 49834

Description: The domain of Limit is a relation. (Contributed by Zhi Wang, 12-Nov-2025.)

Assertion

Ref	Expression
reldmlmd	⊢ Rel dom Limit

Proof of Theorem reldmlmd

Dummy variables 𝑐 𝑑 𝑓 are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-lmd 49832	. 2 ⊢ Limit = (𝑐 ∈ V, 𝑑 ∈ V ↦ (𝑓 ∈ (𝑑 Func 𝑐) ↦ (( oppFunc ‘(𝑐Δfunc𝑑))((oppCat‘𝑐) UP (oppCat‘(𝑑 FuncCat 𝑐)))𝑓)))
2	1	reldmmpo 7490	1 ⊢ Rel dom Limit

Syntax hints:  Vcvv 3438   ↦ cmpt 5177  dom cdm 5622  Rel wrel 5627  ‘cfv 6490  (class class class)co 7356  oppCatcoppc 17632   Func cfunc 17776   FuncCat cfuc 17867  Δ_funccdiag 18133   oppFunc coppf 49309   UP cup 49360   Limit clmd 49830

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-10 2146  ax-11 2162  ax-12 2182  ax-ext 2706  ax-sep 5239  ax-nul 5249  ax-pr 5375

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-nf 1785  df-sb 2068  df-mo 2537  df-eu 2567  df-clab 2713  df-cleq 2726  df-clel 2809  df-nfc 2883  df-rab 3398  df-v 3440  df-dif 3902  df-un 3904  df-ss 3916  df-nul 4284  df-if 4478  df-sn 4579  df-pr 4581  df-op 4585  df-br 5097  df-opab 5159  df-xp 5628  df-rel 5629  df-dm 5632  df-oprab 7360  df-mpo 7361  df-lmd 49832

This theorem is referenced by:  lmdfval  49836