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Theorem csb0 4336
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
StepHypRef Expression
1 csbconstg 3844 . 2 (𝐴 ∈ V → 𝐴 / 𝑥∅ = ∅)
2 csbprc 4335 . 2 𝐴 ∈ V → 𝐴 / 𝑥∅ = ∅)
31, 2pm2.61i 185 1 𝐴 / 𝑥∅ = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1543  wcel 2111  Vcvv 3420  csb 3825  c0 4251
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2113  ax-9 2121  ax-ext 2709
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2072  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3422  df-sbc 3709  df-csb 3826  df-dif 3883  df-nul 4252
This theorem is referenced by:  disjdsct  30779  onfrALTlem5  41863  onfrALTlem4  41864  onfrALTlem5VD  42206  onfrALTlem4VD  42207
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