Theorem csbieOLD 3930

Description: Obsolete version of csbie 3929 as of 15-Oct-2024. (Contributed by AV, 2-Dec-2019.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
csbieOLD	⊢ ⦋𝐴 / 𝑥⦌𝐵 = 𝐶

Distinct variable groups:   𝑥,𝐴   𝑥,𝐶

Allowed substitution hint:   𝐵(𝑥)

Proof of Theorem csbieOLD

Step	Hyp	Ref	Expression
1		csbieOLD.1	. 2 ⊢ 𝐴 ∈ V
2		nfcv 2903	. 2 ⊢ Ⅎ𝑥𝐶
3		csbieOLD.2	. 2 ⊢ (𝑥 = 𝐴 → 𝐵 = 𝐶)
4	1, 2, 3	csbief 3928	1 ⊢ ⦋𝐴 / 𝑥⦌𝐵 = 𝐶

Syntax hints:   → wi 4   = wceq 1541   ∈ wcel 2106  Vcvv 3474  ⦋csb 3893

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-ex 1782  df-nf 1786  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-nfc 2885  df-v 3476  df-sbc 3778  df-csb 3894

This theorem is referenced by: (None)