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Theorem csbeq2i 3279
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 11 . . 3  |-  (  T. 
->  B  =  C
)
32csbeq2dv 3278 . 2  |-  (  T. 
->  [_ A  /  x ]_ B  =  [_ A  /  x ]_ C )
43trud 1333 1  |-  [_ A  /  x ]_ B  = 
[_ A  /  x ]_ C
Colors of variables: wff set class
Syntax hints:    T. wtru 1326    = wceq 1653   [_csb 3253
This theorem is referenced by:  csbvarg  3280  csbnest1g  3305  csbsng  3869  csbunig  4025  csbxpg  4908  csbrng  5117  csbresg  5152  csbima12gALT  5217  csbfv12g  5741  csbfv12gALT  5742  csbnegg  9308  disjxpin  24033  csbcnvg  24042  csbdmg  27972  cdleme31so  31250  cdleme31sn  31251  cdleme31sn1  31252  cdleme31se  31253  cdleme31se2  31254  cdleme31sc  31255  cdleme31sde  31256  cdleme31sn2  31260  cdlemkid3N  31804  cdlemkid4  31805
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-sbc 3164  df-csb 3254
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