Theorem nfreu1 2706

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 2518	. 2 |- ( E! x e. A ph <-> E! x ( x e. A /\ ph ) )
2		nfeu1 2090	. 2 |- F/ x E! x ( x e. A /\ ph )
3	1, 2	nfxfr 1523	1 |- F/ x E! x e. A ph

Syntax hints:   /\ wa 104   F/wnf 1509   E!weu 2079   e. wcel 2202   E!wreu 2513

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-ial 1583

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-eu 2082  df-reu 2518

This theorem is referenced by:  riota2df  6003