Theorem nfreu 3114

Description: Bound-variable hypothesis builder for restricted unique existence. (Contributed by NM, 30-Oct-2010.) (Revised by Mario Carneiro, 8-Oct-2016.)

Hypotheses

Ref	Expression
nfreu.1	|- F/_ x A
nfreu.2	|- F/ x ph

Assertion

Ref	Expression
nfreu	|- F/ x E! y e. A ph

Proof of Theorem nfreu

Step	Hyp	Ref	Expression
1		nftru 1730	. . 3 |- F/ y T.
2		nfreu.1	. . . 4 |- F/_ x A
3	2	a1i 11	. . 3 |- ( T. -> F/_ x A )
4		nfreu.2	. . . 4 |- F/ x ph
5	4	a1i 11	. . 3 |- ( T. -> F/ x ph )
6	1, 3, 5	nfreud 3112	. 2 |- ( T. -> F/ x E! y e. A ph )
7	6	trud 1493	1 |- F/ x E! y e. A ph

Syntax hints:   T. wtru 1484   F/wnf 1708   F/_wnfc 2751   E!wreu 2914

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-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

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  df-cleq 2615  df-clel 2618  df-nfc 2753  df-reu 2919

This theorem is referenced by:  sbcreu  3515  reuccats1  13480  2reu7  41191  2reu8  41192