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Metamath Proof Explorer

Theorem csbief

Description: Conversion of implicit substitution to explicit substitution into a class. (Contributed by NM, 26-Nov-2005) (Revised by Mario Carneiro, 13-Oct-2016)

	Ref	Expression
Hypotheses	csbief.1	$⊢ A \in V$
	csbief.2	$⊢ \underline{Ⅎ} x C$
	csbief.3	$⊢ x = A \to B = C$
Assertion	csbief	$⊢ ⦋ A / x ⦌ B = C$

Proof

Step	Hyp	Ref	Expression
1		csbief.1	$⊢ A \in V$
2		csbief.2	$⊢ \underline{Ⅎ} x C$
3		csbief.3	$⊢ x = A \to B = C$
4	2	a1i	$⊢ A \in V \to \underline{Ⅎ} x C$
5	4 3	csbiegf	$⊢ A \in V \to ⦋ A / x ⦌ B = C$
6	1 5	ax-mp	$⊢ ⦋ A / x ⦌ B = C$