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Theorem ss2abdv 3068
 Description: Deduction of abstraction subclass from implication. (Contributed by NM, 29-Jul-2011.)
Hypothesis
Ref Expression
ss2abdv.1
Assertion
Ref Expression
ss2abdv
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem ss2abdv
StepHypRef Expression
1 ss2abdv.1 . . 3
21alrimiv 1796 . 2
3 ss2ab 3063 . 2
42, 3sylibr 132 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1283  cab 2068   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 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-in 2980  df-ss 2987 This theorem is referenced by:  ssopab2  4038  iotass  4914  imadif  5010  imain  5012  opabbrex  5580  ssoprab2  5592  tfr1onlemssrecs  5988  tfrcllemssrecs  6001
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