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Theorem moimi 2013
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 2012 . 2  |-  ( A. x ( ph  ->  ps )  ->  ( E* x ps  ->  E* x ph ) )
2 moimi.1 . 2  |-  ( ph  ->  ps )
31, 2mpg 1385 1  |-  ( E* x ps  ->  E* x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E*wmo 1949
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952
This theorem is referenced by:  moan  2017  moor  2019  mooran1  2020  mooran2  2021  2moex  2034  2euex  2035  2exeu  2040  mosubt  2790  sndisj  3833  disjxsn  3835  mosubopt  4491  funcnvsn  5045  nfunsn  5322  th3qlem2  6375  shftfn  10223
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