MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfreu1 Structured version   Unicode version

Theorem nfreu1 2870
Description:  x is not free in  E! x  e.  A ph. (Contributed by NM, 19-Mar-1997.)
Assertion
Ref Expression
nfreu1  |-  F/ x E! x  e.  A  ph

Proof of Theorem nfreu1
StepHypRef Expression
1 df-reu 2704 . 2  |-  ( E! x  e.  A  ph  <->  E! x ( x  e.  A  /\  ph )
)
2 nfeu1 2290 . 2  |-  F/ x E! x ( x  e.  A  /\  ph )
31, 2nfxfr 1579 1  |-  F/ x E! x  e.  A  ph
Colors of variables: wff set class
Syntax hints:    /\ wa 359   F/wnf 1553    e. wcel 1725   E!weu 2280   E!wreu 2699
This theorem is referenced by:  nfriota1  6549  riota2df  6562  2reu8  27937
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-ex 1551  df-nf 1554  df-eu 2284  df-reu 2704
  Copyright terms: Public domain W3C validator