Theorem reldmoppf 49250

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 49248	. 2 ⊢ oppFunc = (𝑓 ∈ V, 𝑔 ∈ V ↦ if((Rel 𝑔 ∧ Rel dom 𝑔), ⟨𝑓, tpos 𝑔⟩, ∅))
2	1	reldmmpo 7486	1 ⊢ Rel dom oppFunc

Syntax hints:   ∧ wa 395  Vcvv 3437  ∅c0 4282  ifcif 4474  ⟨cop 4581  dom cdm 5619  Rel wrel 5624  tpos ctpos 8161   oppFunc coppf 49247

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-10 2146  ax-11 2162  ax-12 2182  ax-ext 2705  ax-sep 5236  ax-nul 5246  ax-pr 5372

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-nf 1785  df-sb 2068  df-mo 2537  df-eu 2566  df-clab 2712  df-cleq 2725  df-clel 2808  df-nfc 2882  df-rab 3397  df-v 3439  df-dif 3901  df-un 3903  df-ss 3915  df-nul 4283  df-if 4475  df-sn 4576  df-pr 4578  df-op 4582  df-br 5094  df-opab 5156  df-xp 5625  df-rel 5626  df-dm 5629  df-oprab 7356  df-mpo 7357  df-oppf 49248

This theorem is referenced by: (None)