Theorem nfeu1 2056

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 2048	. 2 |- ( E! x ph <-> E. y A. x ( ph <-> x = y ) )
2		nfa1 1555	. . 3 |- F/ x A. x ( ph <-> x = y )
3	2	nfex 1651	. 2 |- F/ x E. y A. x ( ph <-> x = y )
4	1, 3	nfxfr 1488	1 |- F/ x E! x ph

Syntax hints:   <-> wb 105   A.wal 1362   F/wnf 1474   E.wex 1506   E!weu 2045

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-ial 1548

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-eu 2048

This theorem is referenced by:  nfmo1  2057  moaneu  2121  nfreu1  2669  eusv2i  4491  eusv2nf  4492  iota2  5249  sniota  5250  fv3  5584  tz6.12c  5591  eusvobj1  5912