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Theorem cbvriotav 6316
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 1605 . 2  |-  F/ y
ph
2 nfv 1605 . 2  |-  F/ x ps
3 cbvriotav.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
41, 2, 3cbvriota 6315 1  |-  ( iota_ x  e.  A ph )  =  ( iota_ y  e.  A ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    = wceq 1623   iota_crio 6297
This theorem is referenced by:  ordtypecbv  7232  fin23lem27  7954  zorn2g  8130  cnlnadji  22656  nmopadjlei  22668  cvmliftlem15  23829  cvmliftiota  23832  cvmlift2  23847  cvmlift3lem7  23856  cvmlift3  23859  lshpkrlem3  29302  cdleme40v  30658  lcfl7N  31691  lcf1o  31741  lcfrlem39  31771  hdmap1cbv  31993
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-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rex 2549  df-reu 2550  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-riota 6304
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