Theorem nfeu1 2037

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 2029	. 2 |- ( E! x ph <-> E. y A. x ( ph <-> x = y ) )
2		nfa1 1541	. . 3 |- F/ x A. x ( ph <-> x = y )
3	2	nfex 1637	. 2 |- F/ x E. y A. x ( ph <-> x = y )
4	1, 3	nfxfr 1474	1 |- F/ x E! x ph

Syntax hints:   <-> wb 105   A.wal 1351   F/wnf 1460   E.wex 1492   E!weu 2026

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-eu 2029

This theorem is referenced by:  nfmo1  2038  moaneu  2102  nfreu1  2648  eusv2i  4455  eusv2nf  4456  iota2  5206  sniota  5207  fv3  5538  tz6.12c  5545  eusvobj1  5861