Theorem moimi 2068

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

Step	Hyp	Ref	Expression
1		moim 2067	. 2 |- ( A. x ( ph -> ps ) -> ( E* x ps -> E* x ph ) )
2		moimi.1	. 2 |- ( ph -> ps )
3	1, 2	mpg 1428	1 |- ( E* x ps -> E* x ph )

Syntax hints:   -> wi 4   E*wmo 2004

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 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512

This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1740  df-eu 2006  df-mo 2007

This theorem is referenced by:  moan  2072  moor  2074  mooran1  2075  mooran2  2076  2moex  2089  2euex  2090  2exeu  2095  mosubt  2885  sndisj  3957  disjxsn  3959  mosubopt  4644  funcnvsn  5208  nfunsn  5495  th3qlem2  6572  shftfn  10701