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Theorem difrab 3607
 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 2706 . . 3
2 df-rab 2706 . . 3
31, 2difeq12i 3455 . 2
4 df-rab 2706 . . 3
5 difab 3602 . . . 4
6 anass 631 . . . . . 6
7 simpr 448 . . . . . . . . 9
87con3i 129 . . . . . . . 8
98anim2i 553 . . . . . . 7
10 pm3.2 435 . . . . . . . . . 10
1110adantr 452 . . . . . . . . 9
1211con3d 127 . . . . . . . 8
1312imdistani 672 . . . . . . 7
149, 13impbii 181 . . . . . 6
156, 14bitr3i 243 . . . . 5
1615abbii 2547 . . . 4
175, 16eqtr4i 2458 . . 3
184, 17eqtr4i 2458 . 2
193, 18eqtr4i 2458 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359   wceq 1652   wcel 1725  cab 2421  crab 2701   cdif 3309 This theorem is referenced by:  alephsuc3  8447  shftmbl  19425  musum  20968 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rab 2706  df-v 2950  df-dif 3315
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