Theorem mo3 1995

Description: Alternate definition of "at most one." Definition of [BellMachover] p. 460, except that definition has the side condition that y not occur in ph in place of our hypothesis. (Contributed by NM, 8-Mar-1995.)

Hypothesis

Ref	Expression
mo3.1	|- F/ y ph

Assertion

Ref	Expression
mo3	|- ( E* x ph <-> A. x A. y ( ( ph /\ [ y / x ] ph ) -> x = y ) )

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem mo3

Step	Hyp	Ref	Expression
1		mo3.1	. . 3 |- F/ y ph
2	1	nfri 1452	. 2 |- ( ph -> A. y ph )
3	2	mo3h 1994	1 |- ( E* x ph <-> A. x A. y ( ( ph /\ [ y / x ] ph ) -> x = y ) )

Syntax hints:   -> wi 4   /\ wa 102   <-> wb 103   A.wal 1282   F/wnf 1389   [wsb 1685   E*wmo 1942

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686  df-eu 1944  df-mo 1945

This theorem is referenced by:  sbmo  2000  rmo3  2905  isarep2  5006