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Mirrors > Home > MPE Home > Th. List > 2euex | Unicode version |
Description: Double quantification with existential uniqueness. (Contributed by NM, 3-Dec-2001.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
2euex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eu5 2310 | . 2 | |
2 | excom 1849 | . . . 4 | |
3 | nfe1 1840 | . . . . . 6 | |
4 | 3 | nfmo 2301 | . . . . 5 |
5 | 19.8a 1857 | . . . . . . 7 | |
6 | 5 | moimi 2340 | . . . . . 6 |
7 | df-mo 2287 | . . . . . 6 | |
8 | 6, 7 | sylib 196 | . . . . 5 |
9 | 4, 8 | eximd 1882 | . . . 4 |
10 | 2, 9 | syl5bi 217 | . . 3 |
11 | 10 | impcom 430 | . 2 |
12 | 1, 11 | sylbi 195 | 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: 2exeu 2371 |
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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