Theorem nfreu1 2680

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

Step	Hyp	Ref	Expression
1		df-reu 2493	. 2 |- ( E! x e. A ph <-> E! x ( x e. A /\ ph ) )
2		nfeu1 2066	. 2 |- F/ x E! x ( x e. A /\ ph )
3	1, 2	nfxfr 1498	1 |- F/ x E! x e. A ph

Syntax hints:   /\ wa 104   F/wnf 1484   E!weu 2055   e. wcel 2178   E!wreu 2488

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-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-4 1534  ax-ial 1558

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-eu 2058  df-reu 2493

This theorem is referenced by:  riota2df  5943