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Theorem csbriotagOLD 6063
Description: Interchange class substitution and restricted description binder. (Contributed by NM, 24-Feb-2013.) Obsolete as of 2-Sep-2018. Use csbriota 6062 instead. (New usage is discouraged.)
Assertion
Ref Expression
csbriotagOLD  |-  ( A  e.  V  ->  [_ A  /  x ]_ ( iota_ y  e.  B  ph )  =  ( iota_ y  e.  B  [. A  /  x ]. ph ) )
Distinct variable groups:    y, A    x, B    x, y
Allowed substitution hints:    ph( x, y)    A( x)    B( y)    V( x, y)

Proof of Theorem csbriotagOLD
StepHypRef Expression
1 csbriota 6062 . 2  |-  [_ A  /  x ]_ ( iota_ y  e.  B  ph )  =  ( iota_ y  e.  B  [. A  /  x ]. ph )
21a1i 11 1  |-  ( A  e.  V  ->  [_ A  /  x ]_ ( iota_ y  e.  B  ph )  =  ( iota_ y  e.  B  [. A  /  x ]. ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1369    e. wcel 1756   [.wsbc 3184   [_csb 3286   iota_crio 6049
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2422
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-fal 1375  df-ex 1587  df-nf 1590  df-sb 1701  df-eu 2257  df-clab 2428  df-cleq 2434  df-clel 2437  df-nfc 2566  df-ne 2606  df-ral 2718  df-rex 2719  df-v 2972  df-sbc 3185  df-csb 3287  df-dif 3329  df-in 3333  df-ss 3340  df-nul 3636  df-sn 3876  df-uni 4090  df-iota 5379  df-riota 6050
This theorem is referenced by: (None)
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