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Theorem hbeu 1969
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 1396 . . 3  |-  F/ x ph
32nfeu 1967 . 2  |-  F/ x E! y ph
43nfri 1457 1  |-  ( E! y ph  ->  A. x E! y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1287   E!weu 1948
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-eu 1951
This theorem is referenced by:  hbmo  1987  2eu7  2042
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