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Mirrors > Home > MPE Home > Th. List > 2exeu | Unicode version |
Description: Double existential uniqueness implies double uniqueness quantification. (Contributed by NM, 3-Dec-2001.) (Proof shortened by Mario Carneiro, 22-Dec-2016.) |
Ref | Expression |
---|---|
2exeu |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eumo 2313 | . . . 4 | |
2 | euex 2308 | . . . . 5 | |
3 | 2 | moimi 2340 | . . . 4 |
4 | 1, 3 | syl 16 | . . 3 |
5 | 2euex 2366 | . . 3 | |
6 | 4, 5 | anim12ci 567 | . 2 |
7 | eu5 2310 | . 2 | |
8 | 6, 7 | sylibr 212 | 1 |
Colors of variables: wff setvar class |
Syntax hints: -> wi 4 /\ wa 369
E. wex 1612 E! weu 2282 E* wmo 2283 |
This theorem is referenced by: 2eu1 2376 2eu1OLD 2377 2eu2 2378 2eu3 2379 |
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-11 1842 ax-12 1854 ax-13 1999 |
This theorem depends on definitions: df-bi 185 df-an 371 df-tru 1398 df-ex 1613 df-nf 1617 df-eu 2286 df-mo 2287 |
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