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Theorem csbnest1gOLD 3147
Description: Nest the composition of two substitutions. Obsolete as of 11-Nov-2016. (Contributed by NM, 23-May-2006.) (New usage is discouraged.)
Assertion
Ref Expression
csbnest1gOLD  |-  ( ( A  e.  V  /\  A. x  B  e.  W
)  ->  [_ A  /  x ]_ [_ B  /  x ]_ C  =  [_ [_ A  /  x ]_ B  /  x ]_ C
)
Distinct variable group:    x, A
Allowed substitution hints:    B( x)    C( x)    V( x)    W( x)

Proof of Theorem csbnest1gOLD
StepHypRef Expression
1 csbnest1g 3146 . 2  |-  ( A  e.  V  ->  [_ A  /  x ]_ [_ B  /  x ]_ C  = 
[_ [_ A  /  x ]_ B  /  x ]_ C )
21adantr 451 1  |-  ( ( A  e.  V  /\  A. x  B  e.  W
)  ->  [_ A  /  x ]_ [_ B  /  x ]_ C  =  [_ [_ A  /  x ]_ B  /  x ]_ C
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   A.wal 1530    = wceq 1632    e. wcel 1696   [_csb 3094
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-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-sbc 3005  df-csb 3095
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