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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 ∈ V
	Assertion	csbvargi	⊢ ⦋ 𝐴 / 𝑥 ⦌ 𝑥 = 𝐴

Proof

Step	Hyp	Ref	Expression
1		csbvargi.1	⊢ 𝐴 ∈ V
2		csbvarg	⊢ ( 𝐴 ∈ V → ⦋ 𝐴 / 𝑥 ⦌ 𝑥 = 𝐴 )
3	1 2	ax-mp	⊢ ⦋ 𝐴 / 𝑥 ⦌ 𝑥 = 𝐴