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| Description: Two equivalent
expressions for double existential uniqueness.
Curiously, we can put |
| Ref | Expression |
|---|---|
| 2eu8 |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 2eu2 1493 |
. . 3
| |
| 2 | 1 | pm5.32i 656 |
. 2
|
| 3 | hbeu1 1430 |
. . . . 5
| |
| 4 | 3 | hbeu 1431 |
. . . 4
|
| 5 | 4 | euan 1470 |
. . 3
|
| 6 | ancom 446 |
. . . . . 6
| |
| 7 | 6 | eubii 1429 |
. . . . 5
|
| 8 | hbe1 1057 |
. . . . . 6
| |
| 9 | 8 | euan 1470 |
. . . . 5
|
| 10 | ancom 446 |
. . . . 5
| |
| 11 | 7, 9, 10 | 3bitri 184 |
. . . 4
|
| 12 | 11 | eubii 1429 |
. . 3
|
| 13 | ancom 446 |
. . 3
| |
| 14 | 5, 12, 13 | 3bitr4ri 191 |
. 2
|
| 15 | 2eu7 1498 |
. 2
| |
| 16 | 2, 14, 15 | 3bitr3ri 189 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 ax-7 1003 ax-gen 1004 ax-8 1005 ax-10 1007 ax-11 1008 ax-12 1009 ax-17 1012 ax-4 1014 ax-5o 1016 ax-6o 1019 ax-9o 1164 ax-10o 1182 ax-16 1252 ax-11o 1260 |
| This theorem depends on definitions: df-bi 154 df-or 231 df-an 232 df-ex 1022 df-sb 1214 df-eu 1424 df-mo 1425 |