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 ) = ∅ ) |
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 ) = ∅ ) |