Theorem csbieOLD 3945

Description: Obsolete version of csbie 3944 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 3943	1 ⊢ ⦋𝐴 / 𝑥⦌𝐵 = 𝐶

Syntax hints:   → wi 4   = wceq 1537   ∈ wcel 2106  Vcvv 3478  ⦋csb 3908

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-ex 1777  df-nf 1781  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-nfc 2890  df-v 3480  df-sbc 3792  df-csb 3909

This theorem is referenced by: (None)