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

Theorem nfsbc 2902
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 1427 . . 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 2901 . 2  |-  ( T. 
->  F/ x [. A  /  y ]. ph )
76mptru 1325 1  |-  F/ x [. A  /  y ]. ph
Colors of variables: wff set class
Syntax hints:   T. wtru 1317   F/wnf 1421   F/_wnfc 2245   [.wsbc 2882
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-sbc 2883
This theorem is referenced by:  cbvralcsf  3032  cbvrexcsf  3033  opelopabf  4166  ralrnmpt  5530  rexrnmpt  5531  dfopab2  6055  dfoprab3s  6056  mpoxopoveq  6105
  Copyright terms: Public domain W3C validator