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Theorem moimi 1962
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 1961 . 2 (x(φψ) → (∃*xψ∃*xφ))
2 moimi.1 . 2 (φψ)
31, 2mpg 1337 1 (∃*xψ∃*xφ)
Colors of variables: wff set class
Syntax hints:  wi 4  ∃*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-bnd 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:  moan  1966  moor  1968  mooran1  1969  mooran2  1970  2moex  1983  2euex  1984  2exeu  1989  mosubt  2712  sndisj  3751  disjxsn  3753  mosubopt  4348  funcnvsn  4888  nfunsn  5150  th3qlem2  6145
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