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Theorem cbviotav 5416
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 1629 . 2  |-  F/ y
ph
3 nfv 1629 . 2  |-  F/ x ps
41, 2, 3cbviota 5415 1  |-  ( iota
x ph )  =  ( iota y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    = wceq 1652   iotacio 5408
This theorem is referenced by:  oeeui  6837
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-sn 3812  df-uni 4008  df-iota 5410
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