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Theorem csb0 4416
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 3927 . 2 (𝐴 ∈ V → 𝐴 / 𝑥∅ = ∅)
2 csbprc 4415 . 2 𝐴 ∈ V → 𝐴 / 𝑥∅ = ∅)
31, 2pm2.61i 182 1 𝐴 / 𝑥∅ = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1537  wcel 2106  Vcvv 3478  csb 3908  c0 4339
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-sbc 3792  df-csb 3909  df-dif 3966  df-nul 4340
This theorem is referenced by:  disjdsct  32718  onfrALTlem5  44540  onfrALTlem4  44541  onfrALTlem5VD  44883  onfrALTlem4VD  44884
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