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Theorem csbied 3136
Description: Conversion of implicit substitution to explicit substitution into a class. (Contributed by Mario Carneiro, 2-Dec-2014.) (Revised by Mario Carneiro, 13-Oct-2016.)
Hypotheses
Ref Expression
csbied.1  |-  ( ph  ->  A  e.  V )
csbied.2  |-  ( (
ph  /\  x  =  A )  ->  B  =  C )
Assertion
Ref Expression
csbied  |-  ( ph  ->  [_ A  /  x ]_ B  =  C
)
Distinct variable groups:    x, A    x, C    ph, x
Allowed substitution hints:    B( x)    V( x)

Proof of Theorem csbied
StepHypRef Expression
1 nfv 1609 . 2  |-  F/ x ph
2 nfcvd 2433 . 2  |-  ( ph  -> 
F/_ x C )
3 csbied.1 . 2  |-  ( ph  ->  A  e.  V )
4 csbied.2 . 2  |-  ( (
ph  /\  x  =  A )  ->  B  =  C )
51, 2, 3, 4csbiedf 3131 1  |-  ( ph  ->  [_ A  /  x ]_ B  =  C
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    = wceq 1632    e. wcel 1696   [_csb 3094
This theorem is referenced by:  csbied2  3137  fvmptd  5622  cantnfval  7385  imasval  13430  ipoval  14273  gsumvalx  14467  mulgfval  14584  isga  14761  symgval  14787  gexval  14905  isirred  15497  psrval  16126  mplval  16189  opsrval  16232  znval  16505  tsmsval2  17828  dvfsumle  19384  dvfsumabs  19386  dvfsumlem1  19389  dvfsum2  19397  itgparts  19410  evlsval  19419  evl1fval  19426  q1pval  19555  r1pval  19558  rlimcnp2  20277  vmaval  20367  fsumdvdscom  20441  fsumvma  20468  logexprlim  20480  dchrval  20489  dchrisumlema  20653  dchrisumlem2  20655  dchrisumlem3  20656  mendval  27594  hlhilset  32749
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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