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Theorem csbeq2i 2946
Description: Formula-building inference rule for class substitution. (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.)
Hypothesis
Ref Expression
csbeq2i.1  |-  B  =  C
Assertion
Ref Expression
csbeq2i  |-  [_ A  /  x ]_ B  = 
[_ A  /  x ]_ C

Proof of Theorem csbeq2i
StepHypRef Expression
1 csbeq2i.1 . . . 4  |-  B  =  C
21a1i 9 . . 3  |-  ( T. 
->  B  =  C
)
32csbeq2dv 2945 . 2  |-  ( T. 
->  [_ A  /  x ]_ B  =  [_ A  /  x ]_ C )
43trud 1296 1  |-  [_ A  /  x ]_ B  = 
[_ A  /  x ]_ C
Colors of variables: wff set class
Syntax hints:    = wceq 1287   T. wtru 1288   [_csb 2922
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-11 1440  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-sbc 2830  df-csb 2923
This theorem is referenced by:  csbvarg  2947  csbnest1g  2972  csbsng  3488  csbunig  3646  csbxpg  4489  csbcnvg  4590  csbdmg  4600  csbresg  4686  csbrng  4860  csbfv12g  5305  csbnegg  7627  iseqf1olemjpcl  9832  iseqf1olemqpcl  9833  iseqf1olemfvp  9834  iseqf1olemqsum  9837
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