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

Theorem notrab 3619
 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 3611 . 2
2 difin 3579 . . 3
3 dfrab3 3618 . . . 4
43difeq2i 3463 . . 3
5 abid2 2554 . . . 4
65difeq1i 3462 . . 3
72, 4, 63eqtr4i 2467 . 2
8 df-rab 2715 . 2
91, 7, 83eqtr4i 2467 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 360   wceq 1653   wcel 1726  cab 2423  crab 2710   cdif 3318   cin 3320 This theorem is referenced by:  rlimrege0  12374  ordtcld1  17262  ordtcld2  17263  lhop1lem  19898  rpvmasumlem  21182  hasheuni  24476  braew  24594 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ral 2711  df-rab 2715  df-v 2959  df-dif 3324  df-in 3328
 Copyright terms: Public domain W3C validator