Definition df-mo 1383

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 1401. For other possible definitions see mo2 1400 and mo4 1403.

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 1381	. 2 wff ∃*xφ
4	1, 2	wex 979	. . 3 wff ∃xφ
5	1, 2	weu 1380	. . 3 wff ∃!xφ
6	4, 5	wi 3	. 2 wff (∃xφ → ∃!xφ)
7	3, 6	wb 146	1 wff (∃*xφ ↔ (∃xφ → ∃!xφ))

This definition is referenced by:  mo2 1400  mobid 1404  hbmo1 1406  hbmo 1407  cbvmo 1408  exmoeu 1413  moabs 1415  exmo 1416  moeq 1918

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