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Theorem reupick2 3541

Description: Restricted uniqueness "picks" a member of a subclass. (Contributed by Mario Carneiro, 15-Dec-2013.) (Proof shortened by Mario Carneiro, 19-Nov-2016.)

**Assertion**
Ref	Expression
reupick2	$/\$ $/\$ $/\$

Distinct variable group:

Allowed substitution hints:

(

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(

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**Proof of Theorem reupick2**
Step	Hyp	Ref	Expression
1		ancr 532	. . . . . 6 $/\$
2	1	ralimi 2689	. . . . 5 $/\$
3		rexim 2718	. . . . 5 $/\$ $/\$
4	2, 3	syl 15	. . . 4 $/\$
5		reupick3 3540	. . . . . 6 $/\$ $/\$ $/\$
6	5	3exp 1150	. . . . 5 $/\$
7	6	com12 27	. . . 4 $/\$
8	4, 7	syl6 29	. . 3
9	8	3imp1 1164	. 2 $/\$ $/\$ $/\$
10		rsp 2674	. . . 4
11	10	3ad2ant1 976	. . 3 $/\$ $/\$
12	11	imp 418	. 2 $/\$ $/\$ $/\$
13	9, 12	impbid 183	1 $/\$ $/\$ $/\$

Colors of variables: wff setvar class

Syntax hints:

wi 4

wb 176 $/\$ wa 358 $/\$ w3a 934

wcel 1710

wral 2614

wrex 2615

wreu 2616

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925

This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-mo 2209 df-ral 2619 df-rex 2620 df-reu 2621

This theorem is referenced by: (None)

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