Metamath Proof Explorer


Theorem iedgvalprc

Description: Degenerated case 4 for edges: The set of indexed edges of a proper class is the empty set. (Contributed by AV, 12-Oct-2020)

Ref Expression
Assertion iedgvalprc ( 𝐶 ∉ V → ( iEdg ‘ 𝐶 ) = ∅ )

Proof

Step Hyp Ref Expression
1 df-nel ( 𝐶 ∉ V ↔ ¬ 𝐶 ∈ V )
2 fvprc ( ¬ 𝐶 ∈ V → ( iEdg ‘ 𝐶 ) = ∅ )
3 1 2 sylbi ( 𝐶 ∉ V → ( iEdg ‘ 𝐶 ) = ∅ )