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Metamath Proof Explorer

Theorem csb0

Description: The proper substitution of a class into the empty set is the empty set. (Contributed by NM, 18-Aug-2018)

		Ref	Expression
	Assertion	csb0	$⊢ ⦋ A / x ⦌ \emptyset = \emptyset$

Step	Hyp	Ref	Expression
1		csbconstg	$⊢ A \in V \to ⦋ A / x ⦌ \emptyset = \emptyset$
2		csbprc	$⊢ \neg A \in V \to ⦋ A / x ⦌ \emptyset = \emptyset$
3	1 2	pm2.61i	$⊢ ⦋ A / x ⦌ \emptyset = \emptyset$