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Mirrors > Home > NFE Home > Th. List > syldan | Unicode version |
Description: A syllogism deduction with conjoined antecedents. (Contributed by NM, 24-Feb-2005.) (Proof shortened by Wolf Lammen, 6-Apr-2013.) |
Ref | Expression |
---|---|
syldan.1 | |
syldan.2 |
Ref | Expression |
---|---|
syldan |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syldan.1 | . 2 | |
2 | syldan.2 | . . . 4 | |
3 | 2 | expcom 424 | . . 3 |
4 | 3 | adantrd 454 | . 2 |
5 | 1, 4 | mpcom 32 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 358 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 177 df-an 360 |
This theorem is referenced by: sylan2 460 sbcied2 3083 csbied2 3179 lefinaddc 4450 vfinncvntsp 4549 addlec 6208 nchoicelem5 6293 |
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