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Theorem csbprc 3439
 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 3032 . 2
2 sbcex 2945 . . . . . . 7
32con3i 622 . . . . . 6
43pm2.21d 609 . . . . 5
5 falim 1349 . . . . 5
64, 5impbid1 141 . . . 4
76abbidv 2275 . . 3
8 fal 1342 . . . 4
98abf 3437 . . 3
107, 9eqtrdi 2206 . 2
111, 10syl5eq 2202 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1335   wfal 1340   wcel 2128  cab 2143  cvv 2712  wsbc 2937  csb 3031  c0 3394 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-fal 1341  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-sbc 2938  df-csb 3032  df-dif 3104  df-in 3108  df-ss 3115  df-nul 3395 This theorem is referenced by: (None)
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