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Theorem moimi 2065
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 2064 . 2 (∀𝑥(𝜑𝜓) → (∃*𝑥𝜓 → ∃*𝑥𝜑))
2 moimi.1 . 2 (𝜑𝜓)
31, 2mpg 1428 1 (∃*𝑥𝜓 → ∃*𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  ∃*wmo 2001
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004
This theorem is referenced by:  moan  2069  moor  2071  mooran1  2072  mooran2  2073  2moex  2086  2euex  2087  2exeu  2092  mosubt  2864  sndisj  3932  disjxsn  3934  mosubopt  4611  funcnvsn  5175  nfunsn  5462  th3qlem2  6539  shftfn  10627
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