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Theorem csbeq2i 2933
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 2932 . 2  |-  ( T. 
->  [_ A  /  x ]_ B  =  [_ A  /  x ]_ C )
43trud 1294 1  |-  [_ A  /  x ]_ B  = 
[_ A  /  x ]_ C
Colors of variables: wff set class
Syntax hints:    = wceq 1285   T. wtru 1286   [_csb 2909
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-sbc 2817  df-csb 2910
This theorem is referenced by:  csbvarg  2934  csbnest1g  2958  csbsng  3461  csbunig  3617  csbxpg  4447  csbcnvg  4547  csbdmg  4557  csbresg  4643  csbrng  4812  csbfv12g  5241  csbnegg  7373
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