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Theorem csbunig 4015
 Description: Distribute proper substitution through the union of a class. (Contributed by Alan Sare, 10-Nov-2012.)
Assertion
Ref Expression
csbunig

Proof of Theorem csbunig
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 csbabg 3302 . . 3
2 sbcexg 3203 . . . . 5
3 sbcang 3196 . . . . . . 7
4 sbcg 3218 . . . . . . . 8
5 sbcel2g 3264 . . . . . . . 8
64, 5anbi12d 692 . . . . . . 7
73, 6bitrd 245 . . . . . 6
87exbidv 1636 . . . . 5
92, 8bitrd 245 . . . 4
109abbidv 2549 . . 3
111, 10eqtrd 2467 . 2
12 df-uni 4008 . . 3
1312csbeq2i 3269 . 2
14 df-uni 4008 . 2
1511, 13, 143eqtr4g 2492 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wex 1550   wceq 1652   wcel 1725  cab 2421  wsbc 3153  csb 3243  cuni 4007 This theorem is referenced by:  csbfv12gALT  5731  csbfv12gALTVD  28948 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 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-sbc 3154  df-csb 3244  df-uni 4008
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