Theorem mo3 1403

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 1402	. 2 |- (E*xph <-> E.yA.x(ph -> x = y))
3	1	mo 1395	. 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 956   = wceq 958  E.wex 982  [wsbc 1172  E*wmo 1383

This theorem is referenced by:  mo4f 1404  mopick 1435  isarep2 3584

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-11 969  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-eu 1384  df-mo 1385

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