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Theorem hbmo 1912
Description: Bound-variable hypothesis builder for "at most one." (Contributed by NM, 9-Mar-1995.)
Hypothesis
Ref Expression
hbmo.1 (φxφ)
Assertion
Ref Expression
hbmo (∃*yφx∃*yφ)

Proof of Theorem hbmo
StepHypRef Expression
1 df-mo 1877 . 2 (∃*yφ ↔ (yφ∃!yφ))
2 hbmo.1 . . . 4 (φxφ)
32hbex 1500 . . 3 (yφxyφ)
42hbeu 1894 . . 3 (∃!yφx∃!yφ)
53, 4hbim 1410 . 2 ((yφ∃!yφ) → x(yφ∃!yφ))
61, 5hbxfrbi 1334 1 (∃*yφx∃*yφ)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1221  wex 1354  ∃!weu 1873  ∃*wmo 1874
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 614  ax-5 1309  ax-7 1310  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-8 1368  ax-10 1369  ax-11 1370  ax-i12 1371  ax-bnd 1372  ax-4 1373  ax-17 1392  ax-i9 1396  ax-ial 1400  ax-i5r 1401
This theorem depends on definitions:  df-bi 110  df-tru 1226  df-nf 1323  df-sb 1619  df-eu 1876  df-mo 1877
This theorem is referenced by:  moexexdc  1957  2moex  1959  2euex  1960  2exeu  1965
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