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Theorem inrab2 3454
 Description: Intersection with a restricted class abstraction. (Contributed by NM, 19-Nov-2007.)
Assertion
Ref Expression
inrab2
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem inrab2
StepHypRef Expression
1 df-rab 2565 . . 3
2 abid2 2413 . . . 4
32eqcomi 2300 . . 3
41, 3ineq12i 3381 . 2
5 df-rab 2565 . . 3
6 inab 3449 . . . 4
7 elin 3371 . . . . . . 7
87anbi1i 676 . . . . . 6
9 an32 773 . . . . . 6
108, 9bitri 240 . . . . 5
1110abbii 2408 . . . 4
126, 11eqtr4i 2319 . . 3
135, 12eqtr4i 2319 . 2
144, 13eqtr4i 2319 1
 Colors of variables: wff set class Syntax hints:   wa 358   wceq 1632   wcel 1696  cab 2282  crab 2560   cin 3164 This theorem is referenced by:  iooval2  10705  fzval2  10801  smuval2  12689  smueqlem  12697  dfphi2  12858  ordtrest  16948  ordtrest2lem  16949  itg2addnclem2  25004  bsstrs  26249  nbssntrs  26250 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-v 2803  df-in 3172
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