Theorem nfeu1 1971

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 1963	. 2 |- ( E! x ph <-> E. y A. x ( ph <-> x = y ) )
2		nfa1 1489	. . 3 |- F/ x A. x ( ph <-> x = y )
3	2	nfex 1584	. 2 |- F/ x E. y A. x ( ph <-> x = y )
4	1, 3	nfxfr 1418	1 |- F/ x E! x ph

Syntax hints:   <-> wb 104   A.wal 1297   F/wnf 1404   E.wex 1436   E!weu 1960

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-4 1455  ax-ial 1482

This theorem depends on definitions:  df-bi 116  df-nf 1405  df-eu 1963

This theorem is referenced by:  nfmo1  1972  moaneu  2036  nfreu1  2560  eusv2i  4314  eusv2nf  4315  iota2  5050  sniota  5051  fv3  5376  tz6.12c  5383  eusvobj1  5693