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Theorem cbvriotav 6247
Description: Change bound variable in a restricted description binder. (Contributed by NM, 18-Mar-2013.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypothesis
Ref Expression
cbvriotav.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
cbvriotav  |-  ( iota_ x  e.  A  ph )  =  ( iota_ y  e.  A  ps )
Distinct variable groups:    x, A    y, A    ph, y    ps, x
Allowed substitution hints:    ph( x)    ps( y)

Proof of Theorem cbvriotav
StepHypRef Expression
1 nfv 1678 . 2  |-  F/ y
ph
2 nfv 1678 . 2  |-  F/ x ps
3 cbvriotav.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
41, 2, 3cbvriota 6246 1  |-  ( iota_ x  e.  A  ph )  =  ( iota_ y  e.  A  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    = wceq 1374   iota_crio 6235
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-rex 2813  df-sn 4021  df-uni 4239  df-iota 5542  df-riota 6236
This theorem is referenced by:  ordtypecbv  7931  fin23lem27  8697  zorn2g  8872  usgraidx2v  24055  cnlnadji  26657  nmopadjlei  26669  cvmliftlem15  28369  cvmliftiota  28372  cvmlift2  28387  cvmlift3lem7  28396  cvmlift3  28399  usgedgvadf1  31817  usgedgvadf1ALT  31820  lshpkrlem3  33784  cdleme40v  35140  lcfl7N  36173  lcf1o  36223  lcfrlem39  36253  hdmap1cbv  36475
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