Theorem nfreu1 2661

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 2474	. 2 |- ( E! x e. A ph <-> E! x ( x e. A /\ ph ) )
2		nfeu1 2048	. 2 |- F/ x E! x ( x e. A /\ ph )
3	1, 2	nfxfr 1484	1 |- F/ x E! x e. A ph

Syntax hints:   /\ wa 104   F/wnf 1470   E!weu 2037   e. wcel 2159   E!wreu 2469

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 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-4 1520  ax-ial 1544

This theorem depends on definitions:  df-bi 117  df-nf 1471  df-eu 2040  df-reu 2474

This theorem is referenced by:  riota2df  5866