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Theorem abssexg 4138
 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 4136 . 2
2 df-pw 3541 . . . 4
32eleq1i 2220 . . 3
4 simpl 108 . . . . 5
54ss2abi 3196 . . . 4
6 ssexg 4099 . . . 4
75, 6mpan 421 . . 3
83, 7sylbi 120 . 2
91, 8syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wcel 2125  cab 2140  cvv 2709   wss 3098  cpw 3539 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-14 2128  ax-ext 2136  ax-sep 4078  ax-pow 4130 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-v 2711  df-in 3104  df-ss 3111  df-pw 3541 This theorem is referenced by:  pmex  6587  tgval  12396
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