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

Theorem nfsuc 4422
Description: Bound-variable hypothesis builder for successor. (Contributed by NM, 15-Sep-2003.)
Hypothesis
Ref Expression
nfsuc.1  |-  F/_ x A
Assertion
Ref Expression
nfsuc  |-  F/_ x  suc  A

Proof of Theorem nfsuc
StepHypRef Expression
1 df-suc 4385 . 2  |-  suc  A  =  ( A  u.  { A } )
2 nfsuc.1 . . 3  |-  F/_ x A
32nfsn 3666 . . 3  |-  F/_ x { A }
42, 3nfun 3305 . 2  |-  F/_ x
( A  u.  { A } )
51, 4nfcxfr 2328 1  |-  F/_ x  suc  A
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2318    u. cun 3141   {csn 3606   suc csuc 4379
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2170
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2175  df-cleq 2181  df-clel 2184  df-nfc 2320  df-v 2753  df-un 3147  df-sn 3612  df-pr 3613  df-suc 4385
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator