Theorem csbiedOLD 3924

Description: Obsolete version of csbied 3923 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.)

Hypotheses

Ref	Expression
csbiedOLD.1	⊢ (𝜑 → 𝐴 ∈ 𝑉)
csbiedOLD.2	⊢ ((𝜑 ∧ 𝑥 = 𝐴) → 𝐵 = 𝐶)

Assertion

Ref	Expression
csbiedOLD	⊢ (𝜑 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐶)

Distinct variable groups:   𝑥,𝐴   𝑥,𝐶   𝜑,𝑥

Allowed substitution hints:   𝐵(𝑥)   𝑉(𝑥)

Proof of Theorem csbiedOLD

Step	Hyp	Ref	Expression
1		nfv 1909	. 2 ⊢ Ⅎ𝑥𝜑
2		nfcvd 2896	. 2 ⊢ (𝜑 → Ⅎ𝑥𝐶)
3		csbiedOLD.1	. 2 ⊢ (𝜑 → 𝐴 ∈ 𝑉)
4		csbiedOLD.2	. 2 ⊢ ((𝜑 ∧ 𝑥 = 𝐴) → 𝐵 = 𝐶)
5	1, 2, 3, 4	csbiedf 3916	1 ⊢ (𝜑 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐶)

Syntax hints:   → wi 4   ∧ wa 395   = wceq 1533   ∈ wcel 2098  ⦋csb 3885

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2695

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-nfc 2877  df-v 3468  df-sbc 3770  df-csb 3886

This theorem is referenced by: (None)