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Theorem nfreu 2727
Description: Bound-variable hypothesis builder for restricted uniqueness. (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
StepHypRef Expression
1 nftru 1544 . . 3  |-  F/ y  T.
2 nfreu.1 . . . 4  |-  F/_ x A
32a1i 10 . . 3  |-  (  T. 
->  F/_ x A )
4 nfreu.2 . . . 4  |-  F/ x ph
54a1i 10 . . 3  |-  (  T. 
->  F/ x ph )
61, 3, 5nfreud 2725 . 2  |-  (  T. 
->  F/ x E! y  e.  A  ph )
76trud 1314 1  |-  F/ x E! y  e.  A  ph
Colors of variables: wff set class
Syntax hints:    T. wtru 1307   F/wnf 1534   F/_wnfc 2419   E!wreu 2558
This theorem is referenced by:  sbcreug  3080  2reu7  28072  2reu8  28073
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-cleq 2289  df-clel 2292  df-nfc 2421  df-reu 2563
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