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Theorem euimmo 1964
Description: Uniqueness implies "at most one" through implication. (Contributed by NM, 22-Apr-1995.)
Assertion
Ref Expression
euimmo (x(φψ) → (∃!xψ∃*xφ))

Proof of Theorem euimmo
StepHypRef Expression
1 eumo 1929 . 2 (∃!xψ∃*xψ)
2 moim 1961 . 2 (x(φψ) → (∃*xψ∃*xφ))
31, 2syl5 28 1 (x(φψ) → (∃!xψ∃*xφ))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240  ∃!weu 1897  ∃*wmo 1898
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901
This theorem is referenced by:  euim  1965  2eumo  1985  reuss2  3211
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