2exeu - Intuitionistic Logic Explorer

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Theorem 2exeu 1992

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

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

**Proof of Theorem 2exeu**
Step	Hyp	Ref	Expression
1		excom 1554	. . . . 5
2		hbe1 1384	. . . . . . . 8
3	2	hbmo 1939	. . . . . . 7
4	3	19.41h 1575	. . . . . 6 $/\$ $/\$
5		19.8a 1482	. . . . . . . . 9
6	5	moimi 1965	. . . . . . . 8
7	6	anim2i 324	. . . . . . 7 $/\$ $/\$
8	7	eximi 1491	. . . . . 6 $/\$ $/\$
9	4, 8	sylbir 125	. . . . 5 $/\$ $/\$
10	1, 9	sylanb 268	. . . 4 $/\$ $/\$
11		simpl 102	. . . . . 6 $/\$
12	11	moimi 1965	. . . . 5 $/\$
13	12	adantl 262	. . . 4 $/\$ $/\$
14	10, 13	anim12i 321	. . 3 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
15	14	ancoms 255	. 2 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
16		eu5 1947	. . 3 $/\$
17		eu5 1947	. . 3 $/\$
18	16, 17	anbi12i 433	. 2 $/\$ $/\$ $/\$ $/\$
19		eu5 1947	. . 3 $/\$
20		eu5 1947	. . . . 5 $/\$
21	20	exbii 1496	. . . 4 $/\$
22	20	mobii 1937	. . . 4 $/\$
23	21, 22	anbi12i 433	. . 3 $/\$ $/\$ $/\$ $/\$
24	19, 23	bitri 173	. 2 $/\$ $/\$ $/\$
25	15, 18, 24	3imtr4i 190	1 $/\$

Colors of variables: wff set class

Syntax hints:

wi 4 $/\$ wa 97

wex 1381

weu 1900

wmo 1901

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428

This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904

This theorem is referenced by: (None)