Theorem nfeu1 2030

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 2022	. 2 |- ( E! x ph <-> E. y A. x ( ph <-> x = y ) )
2		nfa1 1534	. . 3 |- F/ x A. x ( ph <-> x = y )
3	2	nfex 1630	. 2 |- F/ x E. y A. x ( ph <-> x = y )
4	1, 3	nfxfr 1467	1 |- F/ x E! x ph

Syntax hints:   <-> wb 104   A.wal 1346   F/wnf 1453   E.wex 1485   E!weu 2019

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

This theorem is referenced by:  nfmo1  2031  moaneu  2095  nfreu1  2641  eusv2i  4440  eusv2nf  4441  iota2  5188  sniota  5189  fv3  5519  tz6.12c  5526  eusvobj1  5840