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Theorem csbeq2i 3029
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 3028 . 2  |-  ( T. 
->  [_ A  /  x ]_ B  =  [_ A  /  x ]_ C )
43mptru 1340 1  |-  [_ A  /  x ]_ B  = 
[_ A  /  x ]_ C
Colors of variables: wff set class
Syntax hints:    = wceq 1331   T. wtru 1332   [_csb 3003
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 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-sbc 2910  df-csb 3004
This theorem is referenced by:  csbvarg  3030  csbnest1g  3055  csbsng  3584  csbunig  3744  csbxpg  4620  csbcnvg  4723  csbdmg  4733  csbresg  4822  csbrng  5000  csbfv12g  5457  csbnegg  7967  iseqf1olemjpcl  10275  iseqf1olemqpcl  10276  iseqf1olemfvp  10277  seq3f1olemqsum  10280
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