Theorem reldmlmd 50484

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 50482	. 2 ⊢ Limit = (𝑐 ∈ V, 𝑑 ∈ V ↦ (𝑓 ∈ (𝑑 Func 𝑐) ↦ (( oppFunc ‘(𝑐Δfunc𝑑))((oppCat‘𝑐) UP (oppCat‘(𝑑 FuncCat 𝑐)))𝑓)))
2	1	reldmmpo 7553	1 ⊢ Rel dom Limit

This proof depends on syntax axioms:  Vcvv 3457   ↦ cmpt 5194  dom cdm 5663  Rel wrel 5668  ‘cfv 6540  (class class class)co 7419  oppCatcoppc 17791   Func cfunc 17935   FuncCat cfuc 18026  Δ_funccdiag 18292   oppFunc coppf 49959   UP cup 50010   Limit clmd 50480

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-10 2179  ax-11 2195  ax-12 2216  ax-ext 2737  ax-sep 5259  ax-pr 5406

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-nf 1817  df-sb 2100  df-mo 2569  df-eu 2599  df-clab 2744  df-cleq 2757  df-clel 2840  df-nfc 2914  df-rab 3419  df-v 3459  df-dif 3909  df-un 3911  df-in 3913  df-ss 3923  df-nul 4287  df-if 4490  df-sn 4592  df-pr 4594  df-op 4598  df-br 5112  df-opab 5176  df-xp 5669  df-rel 5670  df-dm 5673  df-oprab 7423  df-mpo 7424  df-lmd 50482

This theorem is used by:  lmdfval  50486