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Mirrors > Home > MPE Home > Th. List > fresison | Structured version Visualization version Unicode version |
Description: "Fresison", one of the syllogisms of Aristotelian logic. No is (PeM), and some is (MiS), therefore some is not (SoP). (In Aristotelian notation, EIO-4: PeM and MiS therefore SoP.) (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.) |
Ref | Expression |
---|---|
fresison.maj | |
fresison.min |
Ref | Expression |
---|---|
fresison |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fresison.min | . 2 | |
2 | simpr 477 | . . 3 | |
3 | fresison.maj | . . . . . 6 | |
4 | 3 | spi 2054 | . . . . 5 |
5 | 4 | con2i 134 | . . . 4 |
6 | 5 | adantr 481 | . . 3 |
7 | 2, 6 | jca 554 | . 2 |
8 | 1, 7 | eximii 1764 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wa 384 wal 1481 wex 1704 |
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-12 2047 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 |
This theorem is referenced by: (None) |
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