Theorem reldmoppf 49021

Description: The domain of oppFunc is a relation. (Contributed by Zhi Wang, 13-Nov-2025.)

Assertion

Ref	Expression
reldmoppf	⊢ Rel dom oppFunc

Proof of Theorem reldmoppf

Dummy variables 𝑓 𝑔 are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-oppf 49020	. 2 ⊢ oppFunc = (𝑓 ∈ V, 𝑔 ∈ V ↦ if((Rel 𝑔 ∧ Rel dom 𝑔), ⟨𝑓, tpos 𝑔⟩, ∅))
2	1	reldmmpo 7539	1 ⊢ Rel dom oppFunc

Syntax hints:   ∧ wa 395  Vcvv 3459  ∅c0 4308  ifcif 4500  ⟨cop 4607  dom cdm 5654  Rel wrel 5659  tpos ctpos 8222  oppFunccoppf 49019

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 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2707  ax-sep 5266  ax-nul 5276  ax-pr 5402

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 2065  df-mo 2539  df-eu 2568  df-clab 2714  df-cleq 2727  df-clel 2809  df-nfc 2885  df-rab 3416  df-v 3461  df-dif 3929  df-un 3931  df-ss 3943  df-nul 4309  df-if 4501  df-sn 4602  df-pr 4604  df-op 4608  df-br 5120  df-opab 5182  df-xp 5660  df-rel 5661  df-dm 5664  df-oprab 7407  df-mpo 7408  df-oppf 49020

This theorem is referenced by: (None)