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

Theorem abssdv 3171
 Description: Deduction of abstraction subclass from implication. (Contributed by NM, 20-Jan-2006.)
Hypothesis
Ref Expression
abssdv.1
Assertion
Ref Expression
abssdv
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem abssdv
StepHypRef Expression
1 abssdv.1 . . 3
21alrimiv 1846 . 2
3 abss 3166 . 2
42, 3sylibr 133 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1329   wcel 1480  cab 2125   wss 3071 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-in 3077  df-ss 3084 This theorem is referenced by:  fmpt  5570  tfrlemibacc  6223  tfrlemibfn  6225  tfr1onlembacc  6239  tfr1onlembfn  6241  tfrcllembacc  6252  tfrcllembfn  6254  eroprf  6522  genipv  7329  hashfacen  10591  metrest  12689
 Copyright terms: Public domain W3C validator