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Theorem csbeq2dv 3268
Description: Formula-building deduction rule for class substitution. (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.)
Hypothesis
Ref Expression
csbeq2dv.1  |-  ( ph  ->  B  =  C )
Assertion
Ref Expression
csbeq2dv  |-  ( ph  ->  [_ A  /  x ]_ B  =  [_ A  /  x ]_ C )
Distinct variable group:    ph, x
Allowed substitution hints:    A( x)    B( x)    C( x)

Proof of Theorem csbeq2dv
StepHypRef Expression
1 nfv 1629 . 2  |-  F/ x ph
2 csbeq2dv.1 . 2  |-  ( ph  ->  B  =  C )
31, 2csbeq2d 3267 1  |-  ( ph  ->  [_ A  /  x ]_ B  =  [_ A  /  x ]_ C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652   [_csb 3243
This theorem is referenced by:  csbeq2i  3269  mpt2mptsx  6406  dmmpt2ssx  6408  fmpt2x  6409  ovmptss  6420  fmpt2co  6422  cantnffval  7610  fsumcom2  12550  ruclem1  12822  natfval  14135  fucval  14147  evlfval  14306  fsumcn  18892  fsum2cn  18893  dvmptfsum  19851  mpfrcl  19931  fprodcom2  25300  bpolylem  26086  bpolyval  26087  cdleme31sde  31119  cdlemeg47rv2  31244
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-sbc 3154  df-csb 3244
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