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Theorem moimi 1947
Description: "At most one" is preserved through implication (notice wff reversal). (Contributed by NM, 15-Feb-2006.)
Hypothesis
Ref Expression
moimi.1 (φψ)
Assertion
Ref Expression
moimi (∃*xψ∃*xφ)

Proof of Theorem moimi
StepHypRef Expression
1 moim 1946 . 2 (x(φψ) → (∃*xψ∃*xφ))
2 moimi.1 . 2 (φψ)
31, 2mpg 1320 1 (∃*xψ∃*xφ)
Colors of variables: wff set class
Syntax hints:  wi 4  ∃*wmo 1883
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-nf 1330  df-sb 1628  df-eu 1885  df-mo 1886
This theorem is referenced by:  moan  1951  moor  1953  mooran1  1954  mooran2  1955  2moex  1968  2euex  1969  2exeu  1974  mosubt  2695  sndisj  3734  disjxsn  3736  mosubopt  4332  funcnvsn  4871  nfunsn  5132  th3qlem2  6120
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