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Theorem hbeu 2027
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 1442 . . 3  |-  F/ x ph
32nfeu 2025 . 2  |-  F/ x E! y ph
43nfri 1499 1  |-  ( E! y ph  ->  A. x E! y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1333   E!weu 2006
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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-eu 2009
This theorem is referenced by:  hbmo  2045  2eu7  2100
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