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Theorem nfcsb 3277
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 1563 . . 3  |-  F/ y  T.
2 nfcsb.1 . . . 4  |-  F/_ x A
32a1i 11 . . 3  |-  (  T. 
->  F/_ x A )
4 nfcsb.2 . . . 4  |-  F/_ x B
54a1i 11 . . 3  |-  (  T. 
->  F/_ x B )
61, 3, 5nfcsbd 3276 . 2  |-  (  T. 
->  F/_ x [_ A  /  y ]_ B
)
76trud 1332 1  |-  F/_ x [_ A  /  y ]_ B
Colors of variables: wff set class
Syntax hints:    T. wtru 1325   F/_wnfc 2558   [_csb 3243
This theorem is referenced by:  cbvralcsf  3303  cbvreucsf  3305  cbvrabcsf  3306  fmptcof  5894  mpt2mptsx  6406  dmmpt2ssx  6408  fmpt2x  6409  fmpt2co  6422  dfmpt2  6429  nfsum  12477  fsum2dlem  12546  fsumcom2  12550  fsumcn  18892  fsum2cn  18893  dvmptfsum  19851  itgsubst  19925  iundisj2f  24022  nfcprod  25229  fprod2dlem  25296  fprodcom2  25300  wdom2d2  27087  cdlemkid  31660  cdlemk19x  31667  cdlemk11t  31670
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-sbc 3154  df-csb 3244
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