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Metamath Proof Explorer

Theorem edgopval

Description: The edges of a graph represented as ordered pair. (Contributed by AV, 1-Jan-2020) (Revised by AV, 13-Oct-2020)

		Ref	Expression
	Assertion	edgopval	$⊢ (V \in W \land E \in X) \to Edg (⟨V, E⟩) = ran E$

Step	Hyp	Ref	Expression
1		edgval	$⊢ Edg (⟨V, E⟩) = ran iEdg (⟨V, E⟩)$
2		opiedgfv	$⊢ (V \in W \land E \in X) \to iEdg (⟨V, E⟩) = E$
3	2	rneqd	$⊢ (V \in W \land E \in X) \to ran iEdg (⟨V, E⟩) = ran E$
4	1 3	eqtrid	$⊢ (V \in W \land E \in X) \to Edg (⟨V, E⟩) = ran E$