Theorem nfeu1 2091

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 2083	. 2 |- ( E! x ph <-> E. y A. x ( ph <-> x = y ) )
2		nfa1 1590	. . 3 |- F/ x A. x ( ph <-> x = y )
3	2	nfex 1686	. 2 |- F/ x E. y A. x ( ph <-> x = y )
4	1, 3	nfxfr 1523	1 |- F/ x E! x ph

Syntax hints:   <-> wb 105   A.wal 1396   F/wnf 1509   E.wex 1541   E!weu 2080

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-ial 1583

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-eu 2083

This theorem is referenced by:  nfmo1  2092  moaneu  2157  nfreu1  2715  eusv2i  4576  eusv2nf  4577  iota2  5342  sniota  5343  fv3  5693  tz6.12c  5700  eusvobj1  6037