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Theorem csbeq2i 3245
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 3244 . 2  |-  (  T. 
->  [_ A  /  x ]_ B  =  [_ A  /  x ]_ C )
43trud 1329 1  |-  [_ A  /  x ]_ B  = 
[_ A  /  x ]_ C
Colors of variables: wff set class
Syntax hints:    T. wtru 1322    = wceq 1649   [_csb 3219
This theorem is referenced by:  csbvarg  3246  csbnest1g  3271  csbsng  3835  csbunig  3991  csbxpg  4872  csbrng  5081  csbresg  5116  csbima12gALT  5181  csbfv12g  5705  csbfv12gALT  5706  csbnegg  9267  disjxpin  23989  csbcnvg  23998  csbdmg  27857  cdleme31so  30873  cdleme31sn  30874  cdleme31sn1  30875  cdleme31se  30876  cdleme31se2  30877  cdleme31sc  30878  cdleme31sde  30879  cdleme31sn2  30883  cdlemkid3N  31427  cdlemkid4  31428
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-sbc 3130  df-csb 3220
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