Theorem moimi 2145

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 2144	. 2 |- ( A. x ( ph -> ps ) -> ( E* x ps -> E* x ph ) )
2		moimi.1	. 2 |- ( ph -> ps )
3	1, 2	mpg 1499	1 |- ( E* x ps -> E* x ph )

Syntax hints:   -> wi 4   E*wmo 2080

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811  df-eu 2082  df-mo 2083

This theorem is referenced by:  moan  2149  moor  2151  mooran1  2152  mooran2  2153  2moex  2166  2euex  2167  2exeu  2172  mosubt  2983  sndisj  4084  disjxsn  4086  mosubopt  4791  fununmo  5372  funcnvsn  5375  nfunsn  5676  th3qlem2  6806  shftfn  11384