2exeu - Intuitionistic Logic Explorer

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Theorem 2exeu 2033

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 1594	. . . . 5
2		hbe1 1424	. . . . . . . 8
3	2	hbmo 1980	. . . . . . 7
4	3	19.41h 1615	. . . . . 6 $/\$ $/\$
5		19.8a 1522	. . . . . . . . 9
6	5	moimi 2006	. . . . . . . 8
7	6	anim2i 334	. . . . . . 7 $/\$ $/\$
8	7	eximi 1531	. . . . . 6 $/\$ $/\$
9	4, 8	sylbir 133	. . . . 5 $/\$ $/\$
10	1, 9	sylanb 278	. . . 4 $/\$ $/\$
11		simpl 107	. . . . . 6 $/\$
12	11	moimi 2006	. . . . 5 $/\$
13	12	adantl 271	. . . 4 $/\$ $/\$
14	10, 13	anim12i 331	. . 3 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
15	14	ancoms 264	. 2 $/\$ $/\$ $/\$ $/\$ $/\$ $/\$
16		eu5 1988	. . 3 $/\$
17		eu5 1988	. . 3 $/\$
18	16, 17	anbi12i 447	. 2 $/\$ $/\$ $/\$ $/\$
19		eu5 1988	. . 3 $/\$
20		eu5 1988	. . . . 5 $/\$
21	20	exbii 1536	. . . 4 $/\$
22	20	mobii 1978	. . . 4 $/\$
23	21, 22	anbi12i 447	. . 3 $/\$ $/\$ $/\$ $/\$
24	19, 23	bitri 182	. 2 $/\$ $/\$ $/\$
25	15, 18, 24	3imtr4i 199	1 $/\$

Colors of variables: wff set class

Syntax hints:

wi 4 $/\$ wa 102

wex 1421

weu 1941

wmo 1942

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468

This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945

This theorem is referenced by: (None)