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Mirrors > Home > MPE Home > Th. List > 2euex | Structured version Visualization version 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 2496 | . 2 | |
2 | excom 2042 | . . . 4 | |
3 | nfe1 2027 | . . . . . 6 | |
4 | 3 | nfmo 2487 | . . . . 5 |
5 | 19.8a 2052 | . . . . . . 7 | |
6 | 5 | moimi 2520 | . . . . . 6 |
7 | df-mo 2475 | . . . . . 6 | |
8 | 6, 7 | sylib 208 | . . . . 5 |
9 | 4, 8 | eximd 2085 | . . . 4 |
10 | 2, 9 | syl5bi 232 | . . 3 |
11 | 10 | impcom 446 | . 2 |
12 | 1, 11 | sylbi 207 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wex 1704 weu 2470 wmo 2471 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-eu 2474 df-mo 2475 |
This theorem is referenced by: 2exeu 2549 |
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