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Metamath Proof Explorer

Theorem pfxnndmnd

Description: The value of a prefix operation for out-of-domain arguments. (This is due to our definition of function values for out-of-domain arguments, see ndmfv ). (Contributed by AV, 3-Dec-2022) (New usage is discouraged.)

		Ref	Expression
	Assertion	pfxnndmnd	$⊢ \neg (S \in V \land L \in ℕ_{0}) \to S prefix L = \emptyset$

Proof

Step	Hyp	Ref	Expression
1		df-pfx	$⊢ prefix = (s \in V, l \in ℕ_{0} ⟼ s substr ⟨0, l⟩)$
2	1	mpondm0	$⊢ \neg (S \in V \land L \in ℕ_{0}) \to S prefix L = \emptyset$