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Theorem csbriotagOLD 6249
Description: Interchange class substitution and restricted description binder. (Contributed by NM, 24-Feb-2013.) Obsolete as of 2-Sep-2018. Use csbriota 6248 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 6248 . 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 1374    e. wcel 1762   [.wsbc 3324   [_csb 3428   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-3an 970  df-tru 1377  df-fal 1380  df-ex 1592  df-nf 1595  df-sb 1707  df-eu 2272  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-ne 2657  df-ral 2812  df-rex 2813  df-v 3108  df-sbc 3325  df-csb 3429  df-dif 3472  df-in 3476  df-ss 3483  df-nul 3779  df-sn 4021  df-uni 4239  df-iota 5542  df-riota 6236
This theorem is referenced by: (None)
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