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Theorem dfrab3ss 3243
 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 2959 . . 3
2 ineq1 3159 . . . 4
32eqcomd 2061 . . 3
41, 3sylbi 118 . 2
5 dfrab3 3241 . 2
6 dfrab3 3241 . . . 4
76ineq2i 3163 . . 3
8 inass 3175 . . 3
97, 8eqtr4i 2079 . 2
104, 5, 93eqtr4g 2113 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1259  cab 2042  crab 2327   cin 2944   wss 2945 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rab 2332  df-v 2576  df-in 2952  df-ss 2959 This theorem is referenced by: (None)
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