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Theorem abssi 3015
 Description: Inference of abstraction subclass from implication. (Contributed by NM, 20-Jan-2006.)
Hypothesis
Ref Expression
abssi.1
Assertion
Ref Expression
abssi
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem abssi
StepHypRef Expression
1 abssi.1 . . 3
21ss2abi 3012 . 2
3 abid2 2158 . 2
42, 3sseqtri 2977 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1393  cab 2026   wss 2917 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-in 2924  df-ss 2931 This theorem is referenced by:  ssab2  3024  abf  3260  intab  3644  opabss  3821  relopabi  4463  exse2  4699  tfrlem8  5934  frecabex  5984  fiprc  6292  nqprxx  6644  ltnqex  6647  gtnqex  6648  recexprlemell  6720  recexprlemelu  6721  recexprlempr  6730
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