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Theorem csbeq2dv 3236
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 3235 1  |-  ( ph  ->  [_ A  /  x ]_ B  =  [_ A  /  x ]_ C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649   [_csb 3211
This theorem is referenced by:  csbeq2i  3237  mpt2mptsx  6373  dmmpt2ssx  6375  fmpt2x  6376  ovmptss  6387  fmpt2co  6389  cantnffval  7574  fsumcom2  12513  ruclem1  12785  natfval  14098  fucval  14110  evlfval  14269  fsumcn  18853  fsum2cn  18854  dvmptfsum  19812  mpfrcl  19892  fprodcom2  25261  bpolylem  25998  bpolyval  25999  cdleme31sde  30867  cdlemeg47rv2  30992
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 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
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 2391  df-cleq 2397  df-clel 2400  df-sbc 3122  df-csb 3212
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