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Theorem abssexg 3962
 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 3961 . 2
2 df-pw 3389 . . . 4
32eleq1i 2119 . . 3
4 simpl 106 . . . . 5
54ss2abi 3040 . . . 4
6 ssexg 3924 . . . 4
75, 6mpan 408 . . 3
83, 7sylbi 118 . 2
91, 8syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wcel 1409  cab 2042  cvv 2574   wss 2945  cpw 3387 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-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3903  ax-pow 3955 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-v 2576  df-in 2952  df-ss 2959  df-pw 3389 This theorem is referenced by: (None)
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