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Theorem csbeq2i 3076
Description: Formula-building inference 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 3075 . 2  |-  ( T. 
->  [_ A  /  x ]_ B  =  [_ A  /  x ]_ C )
43mptru 1357 1  |-  [_ A  /  x ]_ B  = 
[_ A  /  x ]_ C
Colors of variables: wff set class
Syntax hints:    = wceq 1348   T. wtru 1349   [_csb 3049
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-sbc 2956  df-csb 3050
This theorem is referenced by:  csbvarg  3077  csbnest1g  3104  csbsng  3642  csbunig  3802  csbxpg  4690  csbcnvg  4793  csbdmg  4803  csbresg  4892  csbrng  5070  csbfv12g  5530  csbnegg  8104  iseqf1olemjpcl  10438  iseqf1olemqpcl  10439  iseqf1olemfvp  10440  seq3f1olemqsum  10443
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