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Theorem csb0 4342
 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 3885 . 2 (𝐴 ∈ V → 𝐴 / 𝑥∅ = ∅)
2 csbprc 4341 . 2 𝐴 ∈ V → 𝐴 / 𝑥∅ = ∅)
31, 2pm2.61i 185 1 𝐴 / 𝑥∅ = ∅
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538   ∈ wcel 2115  Vcvv 3480  ⦋csb 3866  ∅c0 4276 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 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-fal 1551  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-v 3482  df-sbc 3759  df-csb 3867  df-dif 3922  df-nul 4277 This theorem is referenced by:  disjdsct  30444  onfrALTlem5  41108  onfrALTlem4  41109  onfrALTlem5VD  41451  onfrALTlem4VD  41452
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