Theorem csbie

Description: Conversion of implicit substitution to explicit substitution into a class. (Contributed by AV, 2-Dec-2019)

	Ref	Expression
Hypotheses	csbie.1	⊢ 𝐴 ∈ V
	csbie.2	⊢ ( 𝑥 = 𝐴 → 𝐵 = 𝐶 )
Assertion	csbie	⊢ ⦋ 𝐴 / 𝑥 ⦌ 𝐵 = 𝐶

Proof

Step	Hyp	Ref	Expression
1		csbie.1	⊢ 𝐴 ∈ V
2		csbie.2	⊢ ( 𝑥 = 𝐴 → 𝐵 = 𝐶 )
3		nfcv	⊢ Ⅎ 𝑥 𝐶
4	1 3 2	csbief	⊢ ⦋ 𝐴 / 𝑥 ⦌ 𝐵 = 𝐶