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Theorem csbsng 3422
 Description: Distribute proper substitution through the singleton of a class. (Contributed by Alan Sare, 10-Nov-2012.)
Assertion
Ref Expression
csbsng

Proof of Theorem csbsng
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbabg 2901 . . 3
2 sbceq2g 2866 . . . 4
32abbidv 2152 . . 3
41, 3eqtrd 2069 . 2
5 df-sn 3373 . . 3
65csbeq2i 2870 . 2
7 df-sn 3373 . 2
84, 6, 73eqtr4g 2094 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1242   wcel 1390  cab 2023  wsbc 2758  csb 2846  csn 3367 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-sbc 2759  df-csb 2847  df-sn 3373 This theorem is referenced by: (None)
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