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Theorem csbied 3123
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 1605 . 2  |-  F/ x ph
2 nfcvd 2420 . 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 3118 1  |-  ( ph  ->  [_ A  /  x ]_ B  =  C
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    = wceq 1623    e. wcel 1684   [_csb 3081
This theorem is referenced by:  csbied2  3124  fvmptd  5606  cantnfval  7369  imasval  13414  ipoval  14257  gsumvalx  14451  mulgfval  14568  isga  14745  symgval  14771  gexval  14889  isirred  15481  psrval  16110  mplval  16173  opsrval  16216  znval  16489  tsmsval2  17812  dvfsumle  19368  dvfsumabs  19370  dvfsumlem1  19373  dvfsum2  19381  itgparts  19394  evlsval  19403  evl1fval  19410  q1pval  19539  r1pval  19542  rlimcnp2  20261  vmaval  20351  fsumdvdscom  20425  fsumvma  20452  logexprlim  20464  dchrval  20473  dchrisumlema  20637  dchrisumlem2  20639  dchrisumlem3  20640  mendval  27491  hlhilset  32127
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-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-sbc 2992  df-csb 3082
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