Theorem reldmlmd 49640

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 49638	. 2 ⊢ Limit = (𝑐 ∈ V, 𝑑 ∈ V ↦ (𝑓 ∈ (𝑑 Func 𝑐) ↦ (( oppFunc ‘(𝑐Δfunc𝑑))((oppCat‘𝑐) UP (oppCat‘(𝑑 FuncCat 𝑐)))𝑓)))
2	1	reldmmpo 7526	1 ⊢ Rel dom Limit

Syntax hints:  Vcvv 3450   ↦ cmpt 5191  dom cdm 5641  Rel wrel 5646  ‘cfv 6514  (class class class)co 7390  oppCatcoppc 17679   Func cfunc 17823   FuncCat cfuc 17914  Δ_funccdiag 18180   oppFunc coppf 49115   UP cup 49166   Limit clmd 49636

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-10 2142  ax-11 2158  ax-12 2178  ax-ext 2702  ax-sep 5254  ax-nul 5264  ax-pr 5390

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2066  df-mo 2534  df-eu 2563  df-clab 2709  df-cleq 2722  df-clel 2804  df-nfc 2879  df-rab 3409  df-v 3452  df-dif 3920  df-un 3922  df-ss 3934  df-nul 4300  df-if 4492  df-sn 4593  df-pr 4595  df-op 4599  df-br 5111  df-opab 5173  df-xp 5647  df-rel 5648  df-dm 5651  df-oprab 7394  df-mpo 7395  df-lmd 49638

This theorem is referenced by:  lmdfval  49642