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Theorem csb0 3933
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 3511 . 2 (𝐴 ∈ V → 𝐴 / 𝑥∅ = ∅)
2 csbprc 3931 . 2 𝐴 ∈ V → 𝐴 / 𝑥∅ = ∅)
31, 2pm2.61i 174 1 𝐴 / 𝑥∅ = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1474  wcel 1976  Vcvv 3172  csb 3498  c0 3873
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-fal 1480  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-v 3174  df-sbc 3402  df-csb 3499  df-dif 3542  df-nul 3874
This theorem is referenced by:  disjdsct  28697  onfrALTlem5  37602  onfrALTlem4  37603
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