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Mirrors > Home > ILE Home > Th. List > eueq | Unicode version |
Description: Equality has existential uniqueness. (Contributed by NM, 25-Nov-1994.) |
Ref | Expression |
---|---|
eueq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqtr3 2177 | . . . 4 | |
2 | 1 | gen2 1430 | . . 3 |
3 | 2 | biantru 300 | . 2 |
4 | isset 2718 | . 2 | |
5 | eqeq1 2164 | . . 3 | |
6 | 5 | eu4 2068 | . 2 |
7 | 3, 4, 6 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1333 wceq 1335 wex 1472 weu 2006 wcel 2128 cvv 2712 |
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 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-v 2714 |
This theorem is referenced by: eueq1 2884 moeq 2887 mosubt 2889 reuhypd 4431 mptfng 5295 upxp 12683 |
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