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Mirrors > Home > ILE Home > Th. List > 2eu7 | Unicode version |
Description: Two equivalent expressions for double existential uniqueness. (Contributed by NM, 19-Feb-2005.) |
Ref | Expression |
---|---|
2eu7 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbe1 1475 | . . . 4 | |
2 | 1 | hbeu 2027 | . . 3 |
3 | 2 | euan 2062 | . 2 |
4 | ancom 264 | . . . . 5 | |
5 | 4 | eubii 2015 | . . . 4 |
6 | hbe1 1475 | . . . . 5 | |
7 | 6 | euan 2062 | . . . 4 |
8 | ancom 264 | . . . 4 | |
9 | 5, 7, 8 | 3bitri 205 | . . 3 |
10 | 9 | eubii 2015 | . 2 |
11 | ancom 264 | . 2 | |
12 | 3, 10, 11 | 3bitr4ri 212 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wex 1472 weu 2006 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 |
This theorem is referenced by: (None) |
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