Theorem nfcsb1v 2938

Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by NM, 17-Aug-2006.) (Revised by Mario Carneiro, 12-Oct-2016.)

Assertion

Ref	Expression
nfcsb1v	|- F/_ x [_ A / x ]_ B

Distinct variable group:   x, A

Allowed substitution hint:   B( x)

Proof of Theorem nfcsb1v

Step	Hyp	Ref	Expression
1		nfcv 2219	. 2 |- F/_ x A
2	1	nfcsb1 2937	1 |- F/_ x [_ A / x ]_ B

Syntax hints:   F/_wnfc 2206   [_csb 2908

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-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-sbc 2816  df-csb 2909

This theorem is referenced by:  csbhypf  2941  csbiebt  2942  sbcnestgf  2953  csbnest1g  2957  cbvralcsf  2964  cbvrexcsf  2965  cbvreucsf  2966  cbvrabcsf  2967  csbing  3173  sbcbrg  3834  moop2  4006  pofun  4067  eusvnf  4203  opeliunxp  4413  elrnmpt1  4603  csbima12g  4706  fvmpts  5271  fvmpt2  5275  mptfvex  5277  fmptco  5351  fmptcof  5352  fmptcos  5353  elabrex  5418  fliftfuns  5458  csbov123g  5563  ovmpt2s  5644  mpt2mptsx  5843  dmmpt2ssx  5845  fmpt2x  5846  mpt2fvex  5849  fmpt2co  5857  dfmpt2  5864  f1od2  5876  eqerlem  6160  qliftfuns  6213  nfsum1  10193