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Theorem moimi 1981
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 1980 . 2 (∀𝑥(𝜑𝜓) → (∃*𝑥𝜓 → ∃*𝑥𝜑))
2 moimi.1 . 2 (𝜑𝜓)
31, 2mpg 1356 1 (∃*𝑥𝜓 → ∃*𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  ∃*wmo 1917
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-eu 1919  df-mo 1920
This theorem is referenced by:  moan  1985  moor  1987  mooran1  1988  mooran2  1989  2moex  2002  2euex  2003  2exeu  2008  mosubt  2741  sndisj  3788  disjxsn  3790  mosubopt  4433  funcnvsn  4973  nfunsn  5235  th3qlem2  6240  shftfn  9653
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