Theorem moimi 2152

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 2151	. 2 |- ( A. x ( ph -> ps ) -> ( E* x ps -> E* x ph ) )
2		moimi.1	. 2 |- ( ph -> ps )
3	1, 2	mpg 1504	1 |- ( E* x ps -> E* x ph )

This proof depends on syntax axioms:   -> wi 4   E*wmo 2087

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588

This proof depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-eu 2089  df-mo 2090

This theorem is used by:  moan  2156  moor  2158  mooran1  2159  mooran2  2160  2moex  2173  2euex  2174  2exeu  2179  mosubt  3003  sndisj  4126  disjxsn  4128  mosubopt  4840  fununmo  5423  funcnvsn  5426  nfunsn  5733  th3qlem2  6912  shftfn  11589