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Theorem nfeu 2296
Description: Bound-variable hypothesis builder for uniqueness. Note that 
x and  y needn't be distinct (this makes the proof more difficult). (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
StepHypRef Expression
1 nftru 1563 . . 3  |-  F/ y  T.
2 nfeu.1 . . . 4  |-  F/ x ph
32a1i 11 . . 3  |-  (  T. 
->  F/ x ph )
41, 3nfeud 2294 . 2  |-  (  T. 
->  F/ x E! y
ph )
54trud 1332 1  |-  F/ x E! y ph
Colors of variables: wff set class
Syntax hints:    T. wtru 1325   F/wnf 1553   E!weu 2280
This theorem is referenced by:  2eu7  2366  2eu8  2367  eusv2nf  4713  reusv2lem3  4718  bnj1489  29362
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-eu 2284
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