Theorem nfeu 2486

Description: Bound-variable hypothesis builder for uniqueness. Note that x and y needn't be distinct. (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 7-Oct-2016.)

Hypothesis

Ref	Expression
nfeu.1	|- F/ x ph

Assertion

Ref	Expression
nfeu	|- F/ x E! y ph

Proof of Theorem nfeu

Step	Hyp	Ref	Expression
1		nftru 1730	. . 3 |- F/ y T.
2		nfeu.1	. . . 4 |- F/ x ph
3	2	a1i 11	. . 3 |- ( T. -> F/ x ph )
4	1, 3	nfeud 2484	. 2 |- ( T. -> F/ x E! y ph )
5	4	trud 1493	1 |- F/ x E! y ph

Syntax hints:   T. wtru 1484   F/wnf 1708   E!weu 2470

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-eu 2474

This theorem is referenced by:  2eu7  2559  2eu8  2560  eusv2nf  4864  reusv2lem3  4871  bnj1489  31124  setrec2  42442