ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfre1 Unicode version

Theorem nfre1 2382
Description:  x is not free in  E. x  e.  A ph. (Contributed by NM, 19-Mar-1997.) (Revised by Mario Carneiro, 7-Oct-2016.)
Assertion
Ref Expression
nfre1  |-  F/ x E. x  e.  A  ph

Proof of Theorem nfre1
StepHypRef Expression
1 df-rex 2329 . 2  |-  ( E. x  e.  A  ph  <->  E. x ( x  e.  A  /\  ph )
)
2 nfe1 1401 . 2  |-  F/ x E. x ( x  e.  A  /\  ph )
31, 2nfxfr 1379 1  |-  F/ x E. x  e.  A  ph
Colors of variables: wff set class
Syntax hints:    /\ wa 101   F/wnf 1365   E.wex 1397    e. wcel 1409   E.wrex 2324
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-rex 2329
This theorem is referenced by:  nfiu1  3715  fun11iun  5175  eusvobj2  5526  prarloclem3step  6652  prmuloc2  6723  ltexprlemm  6756  caucvgprprlemaddq  6864  caucvgsrlemgt1  6937  lbzbi  8648  divalglemeunn  10233  divalglemeuneg  10235
  Copyright terms: Public domain W3C validator