2eu3 - New Foundations Explorer

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Theorem 2eu3 2286

Description: Double existential uniqueness. (Contributed by NM, 3-Dec-2001.)

**Assertion**
Ref	Expression
2eu3	$\/$ $/\$ $/\$

**Proof of Theorem 2eu3**
Step	Hyp	Ref	Expression
1		nfmo1 2215	. . . . 5
2	1	19.31 1876	. . . 4 $\/$ $\/$
3	2	albii 1566	. . 3 $\/$ $\/$
4		nfmo1 2215	. . . . 5
5	4	nfal 1842	. . . 4
6	5	19.32 1875	. . 3 $\/$ $\/$
7	3, 6	bitri 240	. 2 $\/$ $\/$
8		2eu1 2284	. . . . . . 7 $/\$
9	8	biimpd 198	. . . . . 6 $/\$
10		ancom 437	. . . . . 6 $/\$ $/\$
11	9, 10	syl6ib 217	. . . . 5 $/\$
12	11	adantld 453	. . . 4 $/\$ $/\$
13		2eu1 2284	. . . . . 6 $/\$
14	13	biimpd 198	. . . . 5 $/\$
15	14	adantrd 454	. . . 4 $/\$ $/\$
16	12, 15	jaoi 368	. . 3 $\/$ $/\$ $/\$
17		2exeu 2281	. . . 4 $/\$
18		2exeu 2281	. . . . 5 $/\$
19	18	ancoms 439	. . . 4 $/\$
20	17, 19	jca 518	. . 3 $/\$ $/\$
21	16, 20	impbid1 194	. 2 $\/$ $/\$ $/\$
22	7, 21	sylbi 187	1 $\/$ $/\$ $/\$

Colors of variables: wff setvar class

Syntax hints:

wi 4

wb 176 $\/$ wo 357 $/\$ wa 358

wal 1540

wex 1541

weu 2204

wmo 2205

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 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-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-mo 2209

This theorem is referenced by: (None)