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Theorem dfrab2 3530
Description: Alternate definition of restricted class abstraction. (Contributed by NM, 20-Sep-2003.)
Assertion
Ref Expression
dfrab2
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem dfrab2
StepHypRef Expression
1 df-rab 2623 . 2
2 inab 3522 . . 3
3 abid2 2470 . . . 4
43ineq1i 3453 . . 3
52, 4eqtr3i 2375 . 2
6 incom 3448 . 2
71, 5, 63eqtri 2377 1
Colors of variables: wff setvar class
Syntax hints:   wa 358   wceq 1642   wcel 1710  cab 2339  crab 2618   cin 3208
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rab 2623  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213
This theorem is referenced by:  phialllem1  4616  frds  5935  nenpw1pwlem1  6084  nmembers1lem1  6268
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