Theorem nfreu1 2481

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 2313	. 2 |- ( E! x e. A ph <-> E! x ( x e. A /\ ph ) )
2		nfeu1 1911	. 2 |- F/ x E! x ( x e. A /\ ph )
3	1, 2	nfxfr 1363	1 |- F/ x E! x e. A ph

Syntax hints:   /\ wa 97   F/wnf 1349   e. wcel 1393   E!weu 1900   E!wreu 2308

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-eu 1903  df-reu 2313

This theorem is referenced by:  riota2df  5488