Theorem nfeu1 1953

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 1945	. 2 |- ( E! x ph <-> E. y A. x ( ph <-> x = y ) )
2		nfa1 1475	. . 3 |- F/ x A. x ( ph <-> x = y )
3	2	nfex 1569	. 2 |- F/ x E. y A. x ( ph <-> x = y )
4	1, 3	nfxfr 1404	1 |- F/ x E! x ph

Syntax hints:   <-> wb 103   A.wal 1283   F/wnf 1390   E.wex 1422   E!weu 1942

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468

This theorem depends on definitions:  df-bi 115  df-nf 1391  df-eu 1945

This theorem is referenced by:  nfmo1  1954  moaneu  2018  nfreu1  2526  eusv2i  4213  eusv2nf  4214  iota2  4923  sniota  4924  fv3  5229  tz6.12c  5235  eusvobj1  5530