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Theorem moimi 2008
Description: "At most one" is preserved through implication (notice wff reversal). (Contributed by NM, 15-Feb-2006.)
Hypothesis
Ref Expression
moimi.1  |-  ( ph  ->  ps )
Assertion
Ref Expression
moimi  |-  ( E* x ps  ->  E* x ph )

Proof of Theorem moimi
StepHypRef Expression
1 moim 2007 . 2  |-  ( A. x ( ph  ->  ps )  ->  ( E* x ps  ->  E* x ph ) )
2 moimi.1 . 2  |-  ( ph  ->  ps )
31, 2mpg 1381 1  |-  ( E* x ps  ->  E* x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E*wmo 1944
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-eu 1946  df-mo 1947
This theorem is referenced by:  moan  2012  moor  2014  mooran1  2015  mooran2  2016  2moex  2029  2euex  2030  2exeu  2035  mosubt  2778  sndisj  3801  disjxsn  3803  mosubopt  4451  funcnvsn  4995  nfunsn  5259  th3qlem2  6296  shftfn  9913
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