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Definition df-eu 2208

Description: Define existential uniqueness, i.e. "there exists exactly one such that ." Definition 10.1 of [BellMachover] p. 97; also Definition *14.02 of [WhiteheadRussell] p. 175. Other possible definitions are given by eu1 2225, eu2 2229, eu3 2230, and eu5 2242 (which in some cases we show with a hypothesis in place of a distinct variable condition on and ). Double uniqueness is tricky: does not mean "exactly one and one " (see 2eu4 2287). (Contributed by NM, 12-Aug-1993.)

Assertion

Ref	Expression
df-eu

Distinct variable groups:   ,   , Allowed substitution hint:   ()

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Detailed syntax breakdown of Definition df-eu

Step	Hyp	Ref	Expression
1		wph	. . 3
2		vx	. . 3
3	1, 2	weu 2204	. 2
4		vy	. . . . . 6
5	2, 4	weq 1643	. . . . 5
6	1, 5	wb 176	. . . 4
7	6, 2	wal 1540	. . 3
8	7, 4	wex 1541	. 2
9	3, 8	wb 176	1

Colors of variables: wff setvar class

This definition is referenced by:  euf  2210  eubid  2211  nfeu1  2214  nfeud2  2216  sb8eu  2222  exists1  2293  reu6  3025  euabsn2  3791  dfeu2  4333  iotauni  4351  iota1  4353  iotanul  4354  iotaex  4356  iota4  4357  fv3  5341

Copyright terms: Public domain

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