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Theorem abssexg 4413
 Description: Existence of a class of subsets. (Contributed by NM, 15-Jul-2006.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
abssexg
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem abssexg
StepHypRef Expression
1 pwexg 4412 . 2
2 df-pw 3825 . . . 4
32eleq1i 2505 . . 3
4 simpl 445 . . . . 5
54ss2abi 3401 . . . 4
6 ssexg 4378 . . . 4
75, 6mpan 653 . . 3
83, 7sylbi 189 . 2
91, 8syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wcel 1727  cab 2428  cvv 2962   wss 3306  cpw 3823 This theorem is referenced by:  pmex  7052  tgval  17051 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-sep 4355  ax-pow 4406 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 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-v 2964  df-in 3313  df-ss 3320  df-pw 3825
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