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Theorem csb0 3934
 Description: The proper substitution of a class into the empty set is empty. (Contributed by NM, 18-Aug-2018.)
Assertion
Ref Expression
csb0 𝐴 / 𝑥∅ = ∅

Proof of Theorem csb0
StepHypRef Expression
1 csbconstg 3512 . 2 (𝐴 ∈ V → 𝐴 / 𝑥∅ = ∅)
2 csbprc 3932 . 2 𝐴 ∈ V → 𝐴 / 𝑥∅ = ∅)
31, 2pm2.61i 175 1 𝐴 / 𝑥∅ = ∅
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475   ∈ wcel 1977  Vcvv 3173  ⦋csb 3499  ∅c0 3874 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-fal 1481  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-sbc 3403  df-csb 3500  df-dif 3543  df-nul 3875 This theorem is referenced by:  disjdsct  28863  onfrALTlem5  37778  onfrALTlem4  37779
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