Theorem reldmoppf 49616

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 49614	. 2 ⊢ oppFunc = (𝑓 ∈ V, 𝑔 ∈ V ↦ if((Rel 𝑔 ∧ Rel dom 𝑔), ⟨𝑓, tpos 𝑔⟩, ∅))
2	1	reldmmpo 7496	1 ⊢ Rel dom oppFunc

Syntax hints:   ∧ wa 395  Vcvv 3430  ∅c0 4274  ifcif 4467  ⟨cop 4574  dom cdm 5626  Rel wrel 5631  tpos ctpos 8170   oppFunc coppf 49613

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 2709  ax-sep 5232  ax-pr 5372

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 2540  df-eu 2570  df-clab 2716  df-cleq 2729  df-clel 2812  df-nfc 2886  df-rab 3391  df-v 3432  df-dif 3893  df-un 3895  df-in 3897  df-ss 3907  df-nul 4275  df-if 4468  df-sn 4569  df-pr 4571  df-op 4575  df-br 5087  df-opab 5149  df-xp 5632  df-rel 5633  df-dm 5636  df-oprab 7366  df-mpo 7367  df-oppf 49614

This theorem is referenced by: (None)