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Mirrors > Home > NFE 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 2372 | . . . 4 | |
2 | 1 | gen2 1547 | . . 3 |
3 | 2 | biantru 491 | . 2 |
4 | isset 2863 | . 2 | |
5 | eqeq1 2359 | . . 3 | |
6 | 5 | eu4 2243 | . 2 |
7 | 3, 4, 6 | 3bitr4i 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wal 1540 wex 1541 wceq 1642 wcel 1710 weu 2204 cvv 2859 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-mo 2209 df-clab 2340 df-cleq 2346 df-clel 2349 df-v 2861 |
This theorem is referenced by: eueq1 3009 moeq 3012 fnopab2g 5206 |
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