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

Theorem cbvabv 2241
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 26-May-1999.)
Hypothesis
Ref Expression
cbvabv.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
cbvabv  |-  { x  |  ph }  =  {
y  |  ps }
Distinct variable groups:    ph, y    ps, x
Allowed substitution hints:    ph( x)    ps( y)

Proof of Theorem cbvabv
StepHypRef Expression
1 nfv 1493 . 2  |-  F/ y
ph
2 nfv 1493 . 2  |-  F/ x ps
3 cbvabv.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
41, 2, 3cbvab 2240 1  |-  { x  |  ph }  =  {
y  |  ps }
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104    = wceq 1316   {cab 2103
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110
This theorem is referenced by:  cdeqab1  2874  difjust  3042  unjust  3044  injust  3046  uniiunlem  3155  dfif3  3457  pwjust  3481  snjust  3502  intab  3770  iotajust  5057  tfrlemi1  6197  tfr1onlemaccex  6213  tfrcllemaccex  6226  frecsuc  6272  isbth  6823  nqprlu  7323  recexpr  7414  caucvgprprlemval  7464  caucvgprprlemnbj  7469  caucvgprprlemaddq  7484  caucvgprprlem1  7485  caucvgprprlem2  7486  axcaucvg  7676  mertensabs  11274  bds  12976
  Copyright terms: Public domain W3C validator