Theorem nfreu1 3110

Description: The setvar 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 2919	. 2 |- ( E! x e. A ph <-> E! x ( x e. A /\ ph ) )
2		nfeu1 2480	. 2 |- F/ x E! x ( x e. A /\ ph )
3	1, 2	nfxfr 1779	1 |- F/ x E! x e. A ph

Syntax hints:   /\ wa 384   F/wnf 1708   e. wcel 1990   E!weu 2470   E!wreu 2914

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710  df-eu 2474  df-reu 2919

This theorem is referenced by:  riota2df  6631  2reu8  41192  iccpartdisj  41373