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Theorem cbvriotav 6490
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 1626 . 2  |-  F/ y
ph
2 nfv 1626 . 2  |-  F/ x ps
3 cbvriotav.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
41, 2, 3cbvriota 6489 1  |-  ( iota_ x  e.  A ph )  =  ( iota_ y  e.  A ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    = wceq 1649   iota_crio 6471
This theorem is referenced by:  ordtypecbv  7412  fin23lem27  8134  zorn2g  8309  usgraidx2v  21271  cnlnadji  23420  nmopadjlei  23432  cvmliftlem15  24757  cvmliftiota  24760  cvmlift2  24775  cvmlift3lem7  24784  cvmlift3  24787  lshpkrlem3  29278  cdleme40v  30634  lcfl7N  31667  lcf1o  31717  lcfrlem39  31747  hdmap1cbv  31969
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 2361
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2235  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-rex 2648  df-reu 2649  df-rab 2651  df-v 2894  df-dif 3259  df-un 3261  df-in 3263  df-ss 3270  df-nul 3565  df-if 3676  df-sn 3756  df-pr 3757  df-op 3759  df-uni 3951  df-br 4147  df-iota 5351  df-fv 5395  df-riota 6478
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