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Metamath Proof Explorer

Theorem csbvargi

Description: The proper substitution of a class for a setvar variable results in the class (if the class exists), in inference form of csbvarg . (Contributed by Giovanni Mascellani, 30-May-2019)

		Ref	Expression
	Hypothesis	csbvargi.1	$⊢ A \in V$
	Assertion	csbvargi	$⊢ ⦋ A / x ⦌ x = A$

Proof

Step	Hyp	Ref	Expression
1		csbvargi.1	$⊢ A \in V$
2		csbvarg	$⊢ A \in V \to ⦋ A / x ⦌ x = A$
3	1 2	ax-mp	$⊢ ⦋ A / x ⦌ x = A$