Theorem nfeu1 2025

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 2017	. 2 |- ( E! x ph <-> E. y A. x ( ph <-> x = y ) )
2		nfa1 1529	. . 3 |- F/ x A. x ( ph <-> x = y )
3	2	nfex 1625	. 2 |- F/ x E. y A. x ( ph <-> x = y )
4	1, 3	nfxfr 1462	1 |- F/ x E! x ph

Syntax hints:   <-> wb 104   A.wal 1341   F/wnf 1448   E.wex 1480   E!weu 2014

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-ial 1522

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-eu 2017

This theorem is referenced by:  nfmo1  2026  moaneu  2090  nfreu1  2637  eusv2i  4433  eusv2nf  4434  iota2  5179  sniota  5180  fv3  5509  tz6.12c  5516  eusvobj1  5829