Theorem nfeu1 2088

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 2080	. 2 |- ( E! x ph <-> E. y A. x ( ph <-> x = y ) )
2		nfa1 1587	. . 3 |- F/ x A. x ( ph <-> x = y )
3	2	nfex 1683	. 2 |- F/ x E. y A. x ( ph <-> x = y )
4	1, 3	nfxfr 1520	1 |- F/ x E! x ph

Syntax hints:   <-> wb 105   A.wal 1393   F/wnf 1506   E.wex 1538   E!weu 2077

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 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-ial 1580

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-eu 2080

This theorem is referenced by:  nfmo1  2089  moaneu  2154  nfreu1  2703  eusv2i  4546  eusv2nf  4547  iota2  5308  sniota  5309  fv3  5650  tz6.12c  5657  eusvobj1  5988