ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  hbs1f Unicode version

Theorem hbs1f 1761
Description: If  x is not free in  ph, it is not free in  [ y  /  x ] ph. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypothesis
Ref Expression
hbs1f.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
hbs1f  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph )

Proof of Theorem hbs1f
StepHypRef Expression
1 hbs1f.1 . . 3  |-  ( ph  ->  A. x ph )
21sbh 1756 . 2  |-  ( [ y  /  x ] ph 
<-> 
ph )
32, 1hbxfrbi 1452 1  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1333   [wsb 1742
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-5 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-4 1490  ax-i9 1510  ax-ial 1514
This theorem depends on definitions:  df-bi 116  df-sb 1743
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator