Theorem nfreu1 2641

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 2455	. 2 |- ( E! x e. A ph <-> E! x ( x e. A /\ ph ) )
2		nfeu1 2030	. 2 |- F/ x E! x ( x e. A /\ ph )
3	1, 2	nfxfr 1467	1 |- F/ x E! x e. A ph

Syntax hints:   /\ wa 103   F/wnf 1453   E!weu 2019   e. wcel 2141   E!wreu 2450

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-eu 2022  df-reu 2455

This theorem is referenced by:  riota2df  5829