Theorem nfreu1 2723

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 2535	. 2 |- ( E! x e. A ph <-> E! x ( x e. A /\ ph ) )
2		nfeu1 2097	. 2 |- F/ x E! x ( x e. A /\ ph )
3	1, 2	nfxfr 1527	1 |- F/ x E! x e. A ph

This proof depends on syntax axioms:   /\ wa 104   F/wnf 1513   E!weu 2086   e. wcel 2209   E!wreu 2530

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-ial 1587

This proof depends on definitions:  df-bi 117  df-nf 1514  df-eu 2089  df-reu 2535

This theorem is used by:  riota2df  6060