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Theorem hbeu 1903
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 (φxφ)
Assertion
Ref Expression
hbeu (∃!yφx∃!yφ)

Proof of Theorem hbeu
StepHypRef Expression
1 hbeu.1 . . . 4 (φxφ)
21nfi 1331 . . 3 xφ
32nfeu 1901 . 2 x∃!yφ
43nfri 1393 1 (∃!yφx∃!yφ)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1226  ∃!weu 1882
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-eu 1885
This theorem is referenced by:  hbmo  1921  2eu7  1976
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