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Theorem csbeq1a 2854
Description: Equality theorem for proper substitution into a class. (Contributed by NM, 10-Nov-2005.)
Assertion
Ref Expression
csbeq1a (x = AB = A / xB)

Proof of Theorem csbeq1a
StepHypRef Expression
1 csbid 2853 . 2 x / xB = B
2 csbeq1 2849 . 2 (x = Ax / xB = A / xB)
31, 2syl5eqr 2083 1 (x = AB = A / xB)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242  csb 2846
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-sbc 2759  df-csb 2847
This theorem is referenced by:  csbhypf  2879  csbiebt  2880  sbcnestgf  2891  cbvralcsf  2902  cbvrexcsf  2903  cbvreucsf  2904  cbvrabcsf  2905  csbing  3138  sbcbrg  3804  moop2  3979  pofun  4040  eusvnf  4151  opeliunxp  4338  elrnmpt1  4528  csbima12g  4629  fvmpts  5193  fvmpt2  5197  mptfvex  5199  fmptco  5273  fmptcof  5274  fmptcos  5275  elabrex  5340  fliftfuns  5381  csbov123g  5485  ovmpt2s  5566  csbopeq1a  5756  mpt2mptsx  5765  dmmpt2ssx  5767  fmpt2x  5768  mpt2fvex  5771  fmpt2co  5779  eqerlem  6073  qliftfuns  6126
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