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

Theorem abssdv 3008
Description: Deduction of abstraction subclass from implication. (Contributed by NM, 20-Jan-2006.)
Hypothesis
Ref Expression
abssdv.1
Assertion
Ref Expression
abssdv  {  |  }  C_
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem abssdv
StepHypRef Expression
1 abssdv.1 . . 3
21alrimiv 1751 . 2
3 abss 3003 . 2  {  |  }  C_
42, 3sylibr 137 1  {  |  }  C_
Colors of variables: wff set class
Syntax hints:   wi 4  wal 1240   wcel 1390   {cab 2023    C_ wss 2911
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-in 2918  df-ss 2925
This theorem is referenced by:  fmpt  5262  tfrlemibacc  5881  tfrlemibfn  5883  eroprf  6135  genipv  6492
  Copyright terms: Public domain W3C validator