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Theorem cbviotav 5365
Description: Change bound variables in a description binder. (Contributed by Andrew Salmon, 1-Aug-2011.)
Hypothesis
Ref Expression
cbviotav.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
cbviotav  |-  ( iota
x ph )  =  ( iota y ps )
Distinct variable groups:    ph, y    ps, x
Allowed substitution hints:    ph( x)    ps( y)

Proof of Theorem cbviotav
StepHypRef Expression
1 cbviotav.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
2 nfv 1626 . 2  |-  F/ y
ph
3 nfv 1626 . 2  |-  F/ x ps
41, 2, 3cbviota 5364 1  |-  ( iota
x ph )  =  ( iota y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    = wceq 1649   iotacio 5357
This theorem is referenced by:  oeeui  6782
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2375  df-cleq 2381  df-clel 2384  df-nfc 2513  df-rex 2656  df-sn 3764  df-uni 3959  df-iota 5359
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