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Theorem nfcsb 2965
Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016.)
Hypotheses
Ref Expression
nfcsb.1  |-  F/_ x A
nfcsb.2  |-  F/_ x B
Assertion
Ref Expression
nfcsb  |-  F/_ x [_ A  /  y ]_ B

Proof of Theorem nfcsb
StepHypRef Expression
1 nftru 1400 . . 3  |-  F/ y T.
2 nfcsb.1 . . . 4  |-  F/_ x A
32a1i 9 . . 3  |-  ( T. 
->  F/_ x A )
4 nfcsb.2 . . . 4  |-  F/_ x B
54a1i 9 . . 3  |-  ( T. 
->  F/_ x B )
61, 3, 5nfcsbd 2964 . 2  |-  ( T. 
->  F/_ x [_ A  /  y ]_ B
)
76mptru 1298 1  |-  F/_ x [_ A  /  y ]_ B
Colors of variables: wff set class
Syntax hints:   T. wtru 1290   F/_wnfc 2215   [_csb 2933
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-sbc 2841  df-csb 2934
This theorem is referenced by:  cbvralcsf  2990  cbvrexcsf  2991  cbvreucsf  2992  cbvrabcsf  2993  fmptcof  5465  mpt2mptsx  5967  dmmpt2ssx  5969  fmpt2x  5970  fmpt2co  5981  dfmpt2  5988  f1od2  6000  nfsum  10742  fsum2dlemstep  10824  fisumcom2  10828
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