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Theorem dfrab3ss 3621
 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 3336 . . 3
2 ineq1 3537 . . . 4
32eqcomd 2443 . . 3
41, 3sylbi 189 . 2
5 dfrab3 3619 . 2
6 dfrab3 3619 . . . 4
76ineq2i 3541 . . 3
8 inass 3553 . . 3
97, 8eqtr4i 2461 . 2
104, 5, 93eqtr4g 2495 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653  cab 2424  crab 2711   cin 3321   wss 3322 This theorem is referenced by:  cusgrasizeindslem2  21485  mbfposadd  26256  proot1hash  27498 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-in 3329  df-ss 3336
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