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Theorem hbmo1 1911
Description: Bound-variable hypothesis builder for "at most one." (Contributed by NM, 8-Mar-1995.)
Assertion
Ref Expression
hbmo1 (∃*xφx∃*xφ)

Proof of Theorem hbmo1
StepHypRef Expression
1 df-mo 1877 . 2 (∃*xφ ↔ (xφ∃!xφ))
2 hbe1 1357 . . 3 (xφxxφ)
3 hbeu1 1883 . . 3 (∃!xφx∃!xφ)
42, 3hbim 1410 . 2 ((xφ∃!xφ) → x(xφ∃!xφ))
51, 4hbxfrbi 1334 1 (∃*xφx∃*xφ)
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-5 1309  ax-7 1310  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-4 1373  ax-ial 1400  ax-i5r 1401
This theorem depends on definitions:  df-bi 110  df-eu 1876  df-mo 1877
This theorem is referenced by:  mopick2  1956  moexexdc  1957
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