MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  csbsng Unicode version

Theorem csbsng 4088
Description: Distribute proper substitution through the singleton of a class. csbsng 4088 is derived from the virtual deduction proof csbsngVD 33693. (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 csbab 3855 . . 3
2 sbceq2g 3833 . . . 4
32abbidv 2593 . . 3
41, 3syl5eq 2510 . 2
5 df-sn 4030 . . 3
65csbeq2i 3836 . 2
7 df-sn 4030 . 2
84, 6, 73eqtr4g 2523 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  {cab 2442  [.wsbc 3327  [_csb 3434  {csn 4029
This theorem is referenced by:  csbprg  4089  csbfv12gALTOLD  33621  csbfv12gALTVD  33699
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-fal 1401  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-sn 4030
  Copyright terms: Public domain W3C validator