Theorem reldmoppf 49629

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 49627	. 2 ⊢ oppFunc = (𝑓 ∈ V, 𝑔 ∈ V ↦ if((Rel 𝑔 ∧ Rel dom 𝑔), ⟨𝑓, tpos 𝑔⟩, ∅))
2	1	reldmmpo 7494	1 ⊢ Rel dom oppFunc

Syntax hints:   ∧ wa 397  Vcvv 3433  ∅c0 4264  ifcif 4457  ⟨cop 4564  dom cdm 5621  Rel wrel 5626  tpos ctpos 8169   oppFunc coppf 49626

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1975  ax-7 2016  ax-8 2123  ax-9 2131  ax-10 2154  ax-11 2170  ax-12 2191  ax-ext 2713  ax-sep 5221  ax-pr 5365

This theorem depends on definitions:  df-bi 209  df-an 398  df-or 855  df-3an 1095  df-tru 1551  df-fal 1561  df-ex 1788  df-nf 1792  df-sb 2075  df-mo 2545  df-eu 2575  df-clab 2720  df-cleq 2733  df-clel 2816  df-nfc 2890  df-rab 3394  df-v 3435  df-dif 3888  df-un 3890  df-in 3892  df-ss 3902  df-nul 4265  df-if 4458  df-sn 4559  df-pr 4561  df-op 4565  df-br 5076  df-opab 5138  df-xp 5627  df-rel 5628  df-dm 5631  df-oprab 7364  df-mpo 7365  df-oppf 49627

This theorem is referenced by: (None)