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Theorem notrab 3353
 Description: Complementation of restricted class abstractions. (Contributed by Mario Carneiro, 3-Sep-2015.)
Assertion
Ref Expression
notrab
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem notrab
StepHypRef Expression
1 difab 3345 . 2
2 difin 3313 . . 3
3 dfrab3 3352 . . . 4
43difeq2i 3191 . . 3
5 abid2 2260 . . . 4
65difeq1i 3190 . . 3
72, 4, 63eqtr4i 2170 . 2
8 df-rab 2425 . 2
91, 7, 83eqtr4i 2170 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 103   wceq 1331   wcel 1480  cab 2125  crab 2420   cdif 3068   cin 3070 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-in1 603  ax-in2 604  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-fal 1337  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rab 2425  df-v 2688  df-dif 3073  df-in 3077 This theorem is referenced by:  diffitest  6781
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