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Mirrors > Home > ILE Home > Th. List > 2euex | Unicode version |
Description: Double quantification with existential uniqueness. (Contributed by NM, 3-Dec-2001.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
2euex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eu5 2044 | . 2 | |
2 | excom 1642 | . . . 4 | |
3 | hbe1 1471 | . . . . . 6 | |
4 | 3 | hbmo 2036 | . . . . 5 |
5 | 19.8a 1569 | . . . . . . 7 | |
6 | 5 | moimi 2062 | . . . . . 6 |
7 | df-mo 2001 | . . . . . 6 | |
8 | 6, 7 | sylib 121 | . . . . 5 |
9 | 4, 8 | eximdh 1590 | . . . 4 |
10 | 2, 9 | syl5bi 151 | . . 3 |
11 | 10 | impcom 124 | . 2 |
12 | 1, 11 | sylbi 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wex 1468 weu 1997 wmo 1998 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 |
This theorem is referenced by: (None) |
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