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Theorem cbvriotav 6332
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 1609 . 2  |-  F/ y
ph
2 nfv 1609 . 2  |-  F/ x ps
3 cbvriotav.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
41, 2, 3cbvriota 6331 1  |-  ( iota_ x  e.  A ph )  =  ( iota_ y  e.  A ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    = wceq 1632   iota_crio 6313
This theorem is referenced by:  ordtypecbv  7248  fin23lem27  7970  zorn2g  8146  cnlnadji  22672  nmopadjlei  22684  cvmliftlem15  23844  cvmliftiota  23847  cvmlift2  23862  cvmlift3lem7  23871  cvmlift3  23874  lshpkrlem3  29924  cdleme40v  31280  lcfl7N  32313  lcf1o  32363  lcfrlem39  32393  hdmap1cbv  32615
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-reu 2563  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-riota 6320
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