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Metamath Proof Explorer

Theorem csbconstgi

Description: The proper substitution of a class for a variable in another variable does not modify it, in inference form. (Contributed by Giovanni Mascellani, 30-May-2019)

		Ref	Expression
	Hypothesis	csbconstgi.1	⊢ 𝐴 ∈ V
	Assertion	csbconstgi	⊢ ⦋ 𝐴 / 𝑥 ⦌ 𝑦 = 𝑦

Proof

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