Theorem csb0 4338

Description: The proper substitution of a class into the empty set is the empty set. (Contributed by NM, 18-Aug-2018.)

Assertion

Ref	Expression
csb0	⊢ ⦋𝐴 / 𝑥⦌∅ = ∅

Proof of Theorem csb0

Step	Hyp	Ref	Expression
1		csbconstg 3847	. 2 ⊢ (𝐴 ∈ V → ⦋𝐴 / 𝑥⦌∅ = ∅)
2		csbprc 4337	. 2 ⊢ (¬ 𝐴 ∈ V → ⦋𝐴 / 𝑥⦌∅ = ∅)
3	1, 2	pm2.61i 182	1 ⊢ ⦋𝐴 / 𝑥⦌∅ = ∅

Syntax hints:   = wceq 1539   ∈ wcel 2108  Vcvv 3422  ⦋csb 3828  ∅c0 4253

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-fal 1552  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-sbc 3712  df-csb 3829  df-dif 3886  df-nul 4254

This theorem is referenced by:  disjdsct  30937  onfrALTlem5  42051  onfrALTlem4  42052  onfrALTlem5VD  42394  onfrALTlem4VD  42395