Definition df-mo 1010

Description: Define "there exists at most one x such that φ". Here we define it in terms of existential uniqueness. Notation of [BellMachover] p. 460, whose definition we show as mo3 1027. For other possible definitions see mo2 1026 and mo4 1029.

Assertion

Ref	Expression
df-mo	⊢ (∃*xφ ↔ (∃xφ → ∃!xφ))

Detailed syntax breakdown of Definition df-mo

Step	Hyp	Ref	Expression
1		wph	. . 3 wff φ
2		vx	. . 3 set x
3	1, 2	wmo 1008	. 2 wff ∃*xφ
4	1, 2	wex 678	. . 3 wff ∃xφ
5	1, 2	weu 1007	. . 3 wff ∃!xφ
6	4, 5	wi 2	. 2 wff (∃xφ → ∃!xφ)
7	3, 6	wb 127	1 wff (∃*xφ ↔ (∃xφ → ∃!xφ))

This definition is referenced by:  mo2 1026  bimod 1030  hbmo1 1032  hbmo 1033  cbvmo 1034  exmoeu 1039  moabs 1041  exmo 1042  moeq 1431

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