Theorem nfeu1 2097

Description: Bound-variable hypothesis builder for uniqueness. (Contributed by NM, 9-Jul-1994.) (Revised by Mario Carneiro, 7-Oct-2016.)

Assertion

Ref	Expression
nfeu1	|- F/ x E! x ph

Proof of Theorem nfeu1

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-eu 2089	. 2 |- ( E! x ph <-> E. y A. x ( ph <-> x = y ) )
2		nfa1 1594	. . 3 |- F/ x A. x ( ph <-> x = y )
3	2	nfex 1690	. 2 |- F/ x E. y A. x ( ph <-> x = y )
4	1, 3	nfxfr 1527	1 |- F/ x E! x ph

Syntax hints:   <-> wb 105   A.wal 1400   F/wnf 1513   E.wex 1545   E!weu 2086

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 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-ial 1587

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-eu 2089

This theorem is referenced by:  nfmo1  2098  moaneu  2163  nfreu1  2723  eusv2i  4596  eusv2nf  4597  iota2  5362  sniota  5363  fv3  5713  tz6.12c  5720  eusvobj1  6062