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Mirrors > Home > MPE Home > Th. List > euan | Unicode version |
Description: Introduction of a conjunct into uniqueness quantifier. (Contributed by NM, 19-Feb-2005.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) (Proof shortened by Wolf Lammen, 24-Dec-2018.) |
Ref | Expression |
---|---|
moanim.1 |
Ref | Expression |
---|---|
euan |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 2308 | . . . 4 | |
2 | moanim.1 | . . . . 5 | |
3 | simpl 457 | . . . . 5 | |
4 | 2, 3 | exlimi 1912 | . . . 4 |
5 | 1, 4 | syl 16 | . . 3 |
6 | ibar 504 | . . . . 5 | |
7 | 2, 6 | eubid 2302 | . . . 4 |
8 | 7 | biimprcd 225 | . . 3 |
9 | 5, 8 | jcai 536 | . 2 |
10 | 7 | biimpa 484 | . 2 |
11 | 9, 10 | impbii 188 | 1 |
Colors of variables: wff setvar class |
Syntax hints: <-> wb 184 /\ wa 369
E. wex 1612 F/ wnf 1616 E! weu 2282 |
This theorem is referenced by: euanv 2355 2eu7 2385 2eu8 2386 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1618 ax-4 1631 ax-5 1704 ax-6 1747 ax-7 1790 ax-10 1837 ax-12 1854 |
This theorem depends on definitions: df-bi 185 df-an 371 df-ex 1613 df-nf 1617 df-eu 2286 |
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