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Theorem csbsng 3867
 Description: Distribute proper substitution through the singleton of a class. csbsng 3867 is derived from the virtual deduction proof csbsngVD 29005. (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 3310 . . 3
2 sbceq2g 3273 . . . 4
32abbidv 2550 . . 3
41, 3eqtrd 2468 . 2
5 df-sn 3820 . . 3
65csbeq2i 3277 . 2
7 df-sn 3820 . 2
84, 6, 73eqtr4g 2493 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  cab 2422  wsbc 3161  csb 3251  csn 3814 This theorem is referenced by:  csbfv12gALT  5739  csbfv12gALTVD  29011 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-sbc 3162  df-csb 3252  df-sn 3820
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