Theorem csb0OLD 4297

Description: Obsolete version of csb0 4296 as of 28-Jun-2024. (Contributed by NM, 18-Aug-2018.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
csb0OLD	⊢ ⦋𝐴 / 𝑥⦌∅ = ∅

Proof of Theorem csb0OLD

Step	Hyp	Ref	Expression
1		csbconstg 3820	. 2 ⊢ (𝐴 ∈ V → ⦋𝐴 / 𝑥⦌∅ = ∅)
2		csbprc 4295	. 2 ⊢ (¬ 𝐴 ∈ V → ⦋𝐴 / 𝑥⦌∅ = ∅)
3	1, 2	pm2.61i 185	1 ⊢ ⦋𝐴 / 𝑥⦌∅ = ∅

Syntax hints:   = wceq 1539   ∈ wcel 2112  Vcvv 3407  ⦋csb 3801  ∅c0 4221

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2114  ax-9 2122  ax-12 2176  ax-ext 2730

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1542  df-fal 1552  df-ex 1783  df-nf 1787  df-sb 2071  df-clab 2737  df-cleq 2751  df-clel 2831  df-nfc 2899  df-v 3409  df-sbc 3694  df-csb 3802  df-dif 3857  df-nul 4222

This theorem is referenced by: (None)