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Theorem difrab 3771
Description: Difference of two restricted class abstractions. (Contributed by NM, 23-Oct-2004.)
Assertion
Ref Expression
difrab

Proof of Theorem difrab
StepHypRef Expression
1 df-rab 2816 . . 3
2 df-rab 2816 . . 3
31, 2difeq12i 3619 . 2
4 df-rab 2816 . . 3
5 difab 3766 . . . 4
6 anass 649 . . . . . 6
7 simpr 461 . . . . . . . . 9
87con3i 135 . . . . . . . 8
98anim2i 569 . . . . . . 7
10 pm3.2 447 . . . . . . . . . 10
1110adantr 465 . . . . . . . . 9
1211con3d 133 . . . . . . . 8
1312imdistani 690 . . . . . . 7
149, 13impbii 188 . . . . . 6
156, 14bitr3i 251 . . . . 5
1615abbii 2591 . . . 4
175, 16eqtr4i 2489 . . 3
184, 17eqtr4i 2489 . 2
193, 18eqtr4i 2489 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442  {crab 2811  \cdif 3472
This theorem is referenced by:  alephsuc3  8976  shftmbl  21949  musum  23467  clwlknclwlkdifs  24960
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478
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