ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfsbc Unicode version

Theorem nfsbc 2860
Description: Bound-variable hypothesis builder for class substitution. (Contributed by NM, 7-Sep-2014.) (Revised by Mario Carneiro, 12-Oct-2016.)
Hypotheses
Ref Expression
nfsbc.1  |-  F/_ x A
nfsbc.2  |-  F/ x ph
Assertion
Ref Expression
nfsbc  |-  F/ x [. A  /  y ]. ph

Proof of Theorem nfsbc
StepHypRef Expression
1 nftru 1400 . . 3  |-  F/ y T.
2 nfsbc.1 . . . 4  |-  F/_ x A
32a1i 9 . . 3  |-  ( T. 
->  F/_ x A )
4 nfsbc.2 . . . 4  |-  F/ x ph
54a1i 9 . . 3  |-  ( T. 
->  F/ x ph )
61, 3, 5nfsbcd 2859 . 2  |-  ( T. 
->  F/ x [. A  /  y ]. ph )
76mptru 1298 1  |-  F/ x [. A  /  y ]. ph
Colors of variables: wff set class
Syntax hints:   T. wtru 1290   F/wnf 1394   F/_wnfc 2215   [.wsbc 2840
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
This theorem is referenced by:  cbvralcsf  2990  cbvrexcsf  2991  opelopabf  4101  ralrnmpt  5441  rexrnmpt  5442  dfopab2  5959  dfoprab3s  5960  mpt2xopoveq  6005
  Copyright terms: Public domain W3C validator