Theorem nfeu1 2090

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 2082	. 2 |- ( E! x ph <-> E. y A. x ( ph <-> x = y ) )
2		nfa1 1589	. . 3 |- F/ x A. x ( ph <-> x = y )
3	2	nfex 1685	. 2 |- F/ x E. y A. x ( ph <-> x = y )
4	1, 3	nfxfr 1522	1 |- F/ x E! x ph

Syntax hints:   <-> wb 105   A.wal 1395   F/wnf 1508   E.wex 1540   E!weu 2079

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 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-4 1558  ax-ial 1582

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-eu 2082

This theorem is referenced by:  nfmo1  2091  moaneu  2156  nfreu1  2705  eusv2i  4552  eusv2nf  4553  iota2  5316  sniota  5317  fv3  5662  tz6.12c  5669  eusvobj1  6004