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Theorem csbprc 3296
 Description: The proper substitution of a proper class for a set into a class results in the empty set. (Contributed by NM, 17-Aug-2018.)
Assertion
Ref Expression
csbprc

Proof of Theorem csbprc
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-csb 2910 . 2
2 sbcex 2824 . . . . . . 7
32con3i 595 . . . . . 6
43pm2.21d 582 . . . . 5
5 falim 1299 . . . . 5
64, 5impbid1 140 . . . 4
76abbidv 2197 . . 3
8 fal 1292 . . . 4
98abf 3294 . . 3
107, 9syl6eq 2130 . 2
111, 10syl5eq 2126 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1285   wfal 1290   wcel 1434  cab 2068  cvv 2602  wsbc 2816  csb 2909  c0 3258 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-sbc 2817  df-csb 2910  df-dif 2976  df-in 2980  df-ss 2987  df-nul 3259 This theorem is referenced by: (None)
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