Theorem nfeu1 1911

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 1903	. 2 |- ( E! x ph <-> E. y A. x ( ph <-> x = y ) )
2		nfa1 1434	. . 3 |- F/ x A. x ( ph <-> x = y )
3	2	nfex 1528	. 2 |- F/ x E. y A. x ( ph <-> x = y )
4	1, 3	nfxfr 1363	1 |- F/ x E! x ph

Syntax hints:   <-> wb 98   A.wal 1241   F/wnf 1349   E.wex 1381   E!weu 1900

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-eu 1903

This theorem is referenced by:  nfmo1  1912  moaneu  1976  nfreu1  2481  eusv2i  4187  eusv2nf  4188  iota2  4893  sniota  4894  fv3  5197  tz6.12c  5203  eusvobj1  5499