Theorem mo3 1399

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:   x,y

Proof of Theorem mo3

Step	Hyp	Ref	Expression
1		mo3.1	. . 3 |- (ph -> A.yph)
2	1	mo2 1398	. 2 |- (E*xph <-> E.yA.x(ph -> x = y))
3	1	mo 1391	. 2 |- (E.yA.x(ph -> x = y) <-> A.xA.y((ph /\ [y / x]ph) -> x = y))
4	2, 3	bitr 173	1 |- (E*xph <-> A.xA.y((ph /\ [y / x]ph) -> x = y))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223  A.wal 952   = wceq 954  E.wex 978  [wsbc 1168  E*wmo 1379

This theorem is referenced by:  mo4f 1400  mopick 1431  isarep2 3570

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-11 965  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170  df-eu 1380  df-mo 1381

Copyright terms: Public domain