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Theorem nfeu 2302
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
StepHypRef Expression
1 nftru 1631 . . 3  |-  F/ y T.
2 nfeu.1 . . . 4  |-  F/ x ph
32a1i 11 . . 3  |-  ( T. 
->  F/ x ph )
41, 3nfeud 2300 . 2  |-  ( T. 
->  F/ x E! y
ph )
54trud 1407 1  |-  F/ x E! y ph
Colors of variables: wff setvar class
Syntax hints:   T. wtru 1399   F/wnf 1621   E!weu 2284
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-eu 2288
This theorem is referenced by:  2eu7  2382  2eu8  2383  eusv2nf  4635  reusv2lem3  4640  bnj1489  34513
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