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Theorem dfrab3ss 3757
 Description: Restricted class abstraction with a common superset. (Contributed by Stefan O'Rear, 12-Sep-2015.) (Proof shortened by Mario Carneiro, 8-Nov-2015.)
Assertion
Ref Expression
dfrab3ss
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem dfrab3ss
StepHypRef Expression
1 df-ss 3456 . . 3
2 ineq1 3663 . . . 4
32eqcomd 2437 . . 3
41, 3sylbi 198 . 2
5 dfrab3 3754 . 2
6 dfrab3 3754 . . . 4
76ineq2i 3667 . . 3
8 inass 3678 . . 3
97, 8eqtr4i 2461 . 2
104, 5, 93eqtr4g 2495 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1437  cab 2414  crab 2786   cin 3441   wss 3442 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-rab 2791  df-v 3089  df-in 3449  df-ss 3456 This theorem is referenced by:  cusgrasizeindslem2  25047  mbfposadd  31692  proot1hash  35776
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