Theorem csbiedOLD

Description: Obsolete version of csbied as of 15-Oct-2024. (Contributed by Mario Carneiro, 2-Dec-2014) (Revised by Mario Carneiro, 13-Oct-2016) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		csbiedOLD.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
2		csbiedOLD.2	⊢ ( ( 𝜑 ∧ 𝑥 = 𝐴 ) → 𝐵 = 𝐶 )
3		nfv	⊢ Ⅎ 𝑥 𝜑
4		nfcvd	⊢ ( 𝜑 → Ⅎ 𝑥 𝐶 )
5	3 4 1 2	csbiedf	⊢ ( 𝜑 → ⦋ 𝐴 / 𝑥 ⦌ 𝐵 = 𝐶 )