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Mirrors > Home > NFE Home > Th. List > euequ1 | Unicode version |
Description: Equality has existential uniqueness. Special case of eueq1 3009 proved using only predicate calculus. (Contributed by Stefan Allan, 4-Dec-2008.) |
Ref | Expression |
---|---|
euequ1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9ev 1656 | . 2 | |
2 | equtr2 1688 | . . 3 | |
3 | 2 | gen2 1547 | . 2 |
4 | equequ1 1684 | . . 3 | |
5 | 4 | eu4 2243 | . 2 |
6 | 1, 3, 5 | mpbir2an 886 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 358 wal 1540 wex 1541 weu 2204 |
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 |
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 |
This theorem is referenced by: copsexg 4607 oprabid 5550 scancan 6331 |
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