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Theorem csbeq2dv 3221
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 1626 . 2  |-  F/ x ph
2 csbeq2dv.1 . 2  |-  ( ph  ->  B  =  C )
31, 2csbeq2d 3220 1  |-  ( ph  ->  [_ A  /  x ]_ B  =  [_ A  /  x ]_ C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649   [_csb 3196
This theorem is referenced by:  csbeq2i  3222  mpt2mptsx  6355  dmmpt2ssx  6357  fmpt2x  6358  ovmptss  6369  fmpt2co  6371  cantnffval  7553  fsumcom2  12487  ruclem1  12759  natfval  14072  fucval  14084  evlfval  14243  fsumcn  18773  fsum2cn  18774  dvmptfsum  19728  mpfrcl  19808  bpolylem  25810  bpolyval  25811  cdleme31sde  30501  cdlemeg47rv2  30626
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2376  df-cleq 2382  df-clel 2385  df-sbc 3107  df-csb 3197
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