ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  euimmo GIF version

Theorem euimmo 1967
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 1932 . 2 (∃!xψ∃*xψ)
2 moim 1964 . 2 (x(φψ) → (∃*xψ∃*xφ))
31, 2syl5 28 1 (x(φψ) → (∃!xψ∃*xφ))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1241  ∃!weu 1900  ∃*wmo 1901
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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428
This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904
This theorem is referenced by:  euim  1968  2eumo  1988  reuss2  3214
  Copyright terms: Public domain W3C validator