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Theorem hbeu 1996
Description: Bound-variable hypothesis builder for uniqueness. Note that 
x and  y needn't be distinct. (Contributed by NM, 8-Mar-1995.) (Proof rewritten by Jim Kingdon, 24-May-2018.)
Hypothesis
Ref Expression
hbeu.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
hbeu  |-  ( E! y ph  ->  A. x E! y ph )

Proof of Theorem hbeu
StepHypRef Expression
1 hbeu.1 . . . 4  |-  ( ph  ->  A. x ph )
21nfi 1421 . . 3  |-  F/ x ph
32nfeu 1994 . 2  |-  F/ x E! y ph
43nfri 1482 1  |-  ( E! y ph  ->  A. x E! y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1312   E!weu 1975
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-eu 1978
This theorem is referenced by:  hbmo  2014  2eu7  2069
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