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  4739  fununmo  5315  funcnvsn  5318  nfunsn  5610  th3qlem2  6724  shftfn  11077