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Theorem csbunig 3744
 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 3061 . . 3
2 sbcexg 2963 . . . . 5
3 sbcang 2952 . . . . . . 7
4 sbcg 2978 . . . . . . . 8
5 sbcel2g 3023 . . . . . . . 8
64, 5anbi12d 464 . . . . . . 7
73, 6bitrd 187 . . . . . 6
87exbidv 1797 . . . . 5
92, 8bitrd 187 . . . 4
109abbidv 2257 . . 3
111, 10eqtrd 2172 . 2
12 df-uni 3737 . . 3
1312csbeq2i 3029 . 2
14 df-uni 3737 . 2
1511, 13, 143eqtr4g 2197 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1331  wex 1468   wcel 1480  cab 2125  wsbc 2909  csb 3003  cuni 3736 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-sbc 2910  df-csb 3004  df-uni 3737 This theorem is referenced by: (None)
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