Theorem nfeu1 2065

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 2057	. 2 |- ( E! x ph <-> E. y A. x ( ph <-> x = y ) )
2		nfa1 1564	. . 3 |- F/ x A. x ( ph <-> x = y )
3	2	nfex 1660	. 2 |- F/ x E. y A. x ( ph <-> x = y )
4	1, 3	nfxfr 1497	1 |- F/ x E! x ph

Syntax hints:   <-> wb 105   A.wal 1371   F/wnf 1483   E.wex 1515   E!weu 2054

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-ial 1557

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-eu 2057

This theorem is referenced by:  nfmo1  2066  moaneu  2130  nfreu1  2678  eusv2i  4502  eusv2nf  4503  iota2  5261  sniota  5262  fv3  5599  tz6.12c  5606  eusvobj1  5931