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Theorem csb0 4145
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 3706 . 2 (𝐴 ∈ V → 𝐴 / 𝑥∅ = ∅)
2 csbprc 4144 . 2 𝐴 ∈ V → 𝐴 / 𝑥∅ = ∅)
31, 2pm2.61i 176 1 𝐴 / 𝑥∅ = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1652  wcel 2155  Vcvv 3350  csb 3693  c0 4081
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-9 2164  ax-10 2183  ax-11 2198  ax-12 2211  ax-13 2352  ax-ext 2743
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 874  df-tru 1656  df-fal 1666  df-ex 1875  df-nf 1879  df-sb 2063  df-clab 2752  df-cleq 2758  df-clel 2761  df-nfc 2896  df-v 3352  df-sbc 3599  df-csb 3694  df-dif 3737  df-nul 4082
This theorem is referenced by:  disjdsct  29932  onfrALTlem5  39423  onfrALTlem4  39424  onfrALTlem5VD  39776  onfrALTlem4VD  39777
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