Theorem reldmcmd 50123

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

Assertion

Ref	Expression
reldmcmd	⊢ Rel dom Colimit

Proof of Theorem reldmcmd

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

Step	Hyp	Ref	Expression
1		df-cmd 50121	. 2 ⊢ Colimit = (𝑐 ∈ V, 𝑑 ∈ V ↦ (𝑓 ∈ (𝑑 Func 𝑐) ↦ ((𝑐Δfunc𝑑)(𝑐 UP (𝑑 FuncCat 𝑐))𝑓)))
2	1	reldmmpo 7501	1 ⊢ Rel dom Colimit

Syntax hints:  Vcvv 3429   ↦ cmpt 5166  dom cdm 5631  Rel wrel 5636  (class class class)co 7367   Func cfunc 17821   FuncCat cfuc 17912  Δ_funccdiag 18178   UP cup 49648   Colimit ccmd 50119

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-10 2147  ax-11 2163  ax-12 2185  ax-ext 2708  ax-sep 5231  ax-pr 5375

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-nf 1786  df-sb 2069  df-mo 2539  df-eu 2569  df-clab 2715  df-cleq 2728  df-clel 2811  df-nfc 2885  df-rab 3390  df-v 3431  df-dif 3892  df-un 3894  df-in 3896  df-ss 3906  df-nul 4274  df-if 4467  df-sn 4568  df-pr 4570  df-op 4574  df-br 5086  df-opab 5148  df-xp 5637  df-rel 5638  df-dm 5641  df-oprab 7371  df-mpo 7372  df-cmd 50121

This theorem is referenced by:  cmdfval  50125