Theorem mo3 1027

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.

Hypothesis

Ref	Expression
mo3.1	|- (ph -> A.yph)

Assertion

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

Distinct variable group(s):   x,y

Proof of Theorem mo3

Step	Hyp	Ref	Expression
1		mo3.1	. . 3 |- (ph -> A.yph)
2	1	mo2 1026	. 2 |- (E*xph <-> E.yA.x(ph -> x = y))
3	1	mo 1020	. 2 |- (E.yA.x(ph -> x = y) <-> A.xA.y((ph /\ [y / x]ph) -> x = y))
4	2, 3	bitr 151	1 |- (E*xph <-> A.xA.y((ph /\ [y / x]ph) -> x = y))

Syntax hints:   -> wi 2   <-> wb 127   /\ wa 196  A.wal 672  E.wex 678   = weq 797  [wsb 852  E*wmo 1008

This theorem is referenced by:  mo4f 1028  mopick 1054

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-eu 1009  df-mo 1010

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