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Theorem csbunig 3899
 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 3197 . . 3
2 sbcexg 3096 . . . . 5
3 sbcang 3089 . . . . . . 7
4 sbcg 3111 . . . . . . . 8
5 sbcel2g 3157 . . . . . . . 8
64, 5anbi12d 691 . . . . . . 7
73, 6bitrd 244 . . . . . 6
87exbidv 1626 . . . . 5
92, 8bitrd 244 . . . 4
109abbidv 2467 . . 3
111, 10eqtrd 2385 . 2
12 df-uni 3892 . . 3
1312csbeq2i 3162 . 2
14 df-uni 3892 . 2
1511, 13, 143eqtr4g 2410 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358  wex 1541   wceq 1642   wcel 1710  cab 2339  wsbc 3046  csb 3136  cuni 3891 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047  df-csb 3137  df-uni 3892 This theorem is referenced by: (None)
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