Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  elssabg Unicode version

Theorem elssabg 3925
 Description: Membership in a class abstraction involving a subset. Unlike elabg 2740, does not have to be a set. (Contributed by NM, 29-Aug-2006.)
Hypothesis
Ref Expression
elssabg.1
Assertion
Ref Expression
elssabg
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem elssabg
StepHypRef Expression
1 ssexg 3919 . . . 4
21expcom 114 . . 3
4 sseq1 3021 . . . 4
5 elssabg.1 . . . 4
64, 5anbi12d 457 . . 3
76elab3g 2745 . 2
83, 7syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103   wceq 1285   wcel 1434  cab 2068  cvv 2602   wss 2974 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3898 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-in 2980  df-ss 2987 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator