Definition df-mo 2209

Description: Define "there exists at most one x such that ph." Here we define it in terms of existential uniqueness. Notation of [BellMachover] p. 460, whose definition we show as mo3 2235. For other possible definitions see mo2 2233 and mo4 2237. (Contributed by NM, 8-Mar-1995.)

Assertion

Ref	Expression
df-mo	|- (E*xph <-> (E.xph -> E!xph))

Detailed syntax breakdown of Definition df-mo

Step	Hyp	Ref	Expression
1		wph	. . 3 wff ph
2		vx	. . 3 setvar x
3	1, 2	wmo 2205	. 2 wff E*xph
4	1, 2	wex 1541	. . 3 wff E.xph
5	1, 2	weu 2204	. . 3 wff E!xph
6	4, 5	wi 4	. 2 wff (E.xph -> E!xph)
7	3, 6	wb 176	1 wff (E*xph <-> (E.xph -> E!xph))

This definition is referenced by:  nfmo1  2215  nfmod2  2217  sb8mo  2223  mo2  2233  mobid  2238  cbvmo  2241  exmoeu  2246  moabs  2248  exmo  2249  2euex  2276  rmo5  2828  moeq  3013  dff3  5421