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Theorem difrab 3753
 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 2791 . . 3
2 df-rab 2791 . . 3
31, 2difeq12i 3587 . 2
4 df-rab 2791 . . 3
5 difab 3748 . . . 4
6 anass 653 . . . . . 6
7 simpr 462 . . . . . . . . 9
87con3i 140 . . . . . . . 8
98anim2i 571 . . . . . . 7
10 pm3.2 448 . . . . . . . . . 10
1110adantr 466 . . . . . . . . 9
1211con3d 138 . . . . . . . 8
1312imdistani 694 . . . . . . 7
149, 13impbii 190 . . . . . 6
156, 14bitr3i 254 . . . . 5
1615abbii 2563 . . . 4
175, 16eqtr4i 2461 . . 3
184, 17eqtr4i 2461 . 2
193, 18eqtr4i 2461 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 370   wceq 1437   wcel 1870  cab 2414  crab 2786   cdif 3439 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ral 2787  df-rab 2791  df-v 3089  df-dif 3445 This theorem is referenced by:  alephsuc3  9003  shftmbl  22360  musum  23974  clwlknclwlkdifs  25524  aciunf1  28096  poimirlem26  31660  poimirlem27  31661
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