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Theorem cbviotav 5225
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 1605 . 2  |-  F/ y
ph
3 nfv 1605 . 2  |-  F/ x ps
41, 2, 3cbviota 5224 1  |-  ( iota
x ph )  =  ( iota y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    = wceq 1623   iotacio 5217
This theorem is referenced by:  oeeui  6600
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rex 2549  df-sn 3646  df-uni 3828  df-iota 5219
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