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Theorem hbeu 1963
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 1392 . . 3  |-  F/ x ph
32nfeu 1961 . 2  |-  F/ x E! y ph
43nfri 1453 1  |-  ( E! y ph  ->  A. x E! y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1283   E!weu 1942
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 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945
This theorem is referenced by:  hbmo  1981  2eu7  2036
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