Theorem moimi 1962

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*xps -> E*xph)

Proof of Theorem moimi

Step	Hyp	Ref	Expression
1		moim 1961	. 2 |- (A.x(ph -> ps) -> (E*xps -> E*xph))
2		moimi.1	. 2 |- (ph -> ps)
3	1, 2	mpg 1337	1 |- (E*xps -> E*xph)

Syntax hints:   -> wi 4  E*wmo 1898

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425

This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901

This theorem is referenced by:  moan  1966  moor  1968  mooran1  1969  mooran2  1970  2moex  1983  2euex  1984  2exeu  1989  mosubt  2712  sndisj  3751  disjxsn  3753  mosubopt  4348  funcnvsn  4888  nfunsn  5150  th3qlem2  6145