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Mirrors > Home > MPE Home > Th. List > mopick2 | Structured version Visualization version Unicode version |
Description: "At most one" can show the existence of a common value. In this case we can infer existence of conjunction from a conjunction of existence, and it is one way to achieve the converse of 19.40 1797. (Contributed by NM, 5-Apr-2004.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
mopick2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfmo1 2481 | . . . 4 | |
2 | nfe1 2027 | . . . 4 | |
3 | 1, 2 | nfan 1828 | . . 3 |
4 | mopick 2535 | . . . . . 6 | |
5 | 4 | ancld 576 | . . . . 5 |
6 | 5 | anim1d 588 | . . . 4 |
7 | df-3an 1039 | . . . 4 | |
8 | 6, 7 | syl6ibr 242 | . . 3 |
9 | 3, 8 | eximd 2085 | . 2 |
10 | 9 | 3impia 1261 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wex 1704 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 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-eu 2474 df-mo 2475 |
This theorem is referenced by: motr 34127 |
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