Theorem moimi 2118

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 2117	. 2 |- ( A. x ( ph -> ps ) -> ( E* x ps -> E* x ph ) )
2		moimi.1	. 2 |- ( ph -> ps )
3	1, 2	mpg 1473	1 |- ( E* x ps -> E* x ph )

Syntax hints:   -> wi 4   E*wmo 2054

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557

This theorem depends on definitions:  df-bi 117  df-nf 1483  df-sb 1785  df-eu 2056  df-mo 2057

This theorem is referenced by:  moan  2122  moor  2124  mooran1  2125  mooran2  2126  2moex  2139  2euex  2140  2exeu  2145  mosubt  2949  sndisj  4039  disjxsn  4041  mosubopt  4738  funcnvsn  5313  nfunsn  5605  th3qlem2  6715  shftfn  11054