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Theorem csb0 4409
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 3908 . 2 (𝐴 ∈ V → 𝐴 / 𝑥∅ = ∅)
2 csbprc 4408 . 2 𝐴 ∈ V → 𝐴 / 𝑥∅ = ∅)
31, 2pm2.61i 182 1 𝐴 / 𝑥∅ = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  wcel 2098  Vcvv 3461  csb 3889  c0 4322
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-v 3463  df-sbc 3774  df-csb 3890  df-dif 3947  df-nul 4323
This theorem is referenced by:  disjdsct  32564  onfrALTlem5  44123  onfrALTlem4  44124  onfrALTlem5VD  44466  onfrALTlem4VD  44467
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