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

Theorem nfsbc 2924
 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
nfsbc.2
Assertion
Ref Expression
nfsbc

Proof of Theorem nfsbc
StepHypRef Expression
1 nftru 1442 . . 3
2 nfsbc.1 . . . 4
32a1i 9 . . 3
4 nfsbc.2 . . . 4
54a1i 9 . . 3
61, 3, 5nfsbcd 2923 . 2
76mptru 1340 1
 Colors of variables: wff set class Syntax hints:   wtru 1332  wnf 1436  wnfc 2266  wsbc 2904 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-sbc 2905 This theorem is referenced by:  cbvralcsf  3057  cbvrexcsf  3058  opelopabf  4191  ralrnmpt  5555  rexrnmpt  5556  dfopab2  6080  dfoprab3s  6081  mpoxopoveq  6130
 Copyright terms: Public domain W3C validator