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Theorem hbeu 2040
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 1455 . . 3  |-  F/ x ph
32nfeu 2038 . 2  |-  F/ x E! y ph
43nfri 1512 1  |-  ( E! y ph  ->  A. x E! y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1346   E!weu 2019
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-eu 2022
This theorem is referenced by:  hbmo  2058  2eu7  2113
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