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Mirrors > Home > NFE Home > Th. List > sylibd | GIF version |
Description: A syllogism deduction. (Contributed by NM, 3-Aug-1994.) |
Ref | Expression |
---|---|
sylibd.1 | ⊢ (φ → (ψ → χ)) |
sylibd.2 | ⊢ (φ → (χ ↔ θ)) |
Ref | Expression |
---|---|
sylibd | ⊢ (φ → (ψ → θ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylibd.1 | . 2 ⊢ (φ → (ψ → χ)) | |
2 | sylibd.2 | . . 3 ⊢ (φ → (χ ↔ θ)) | |
3 | 2 | biimpd 198 | . 2 ⊢ (φ → (χ → θ)) |
4 | 1, 3 | syld 40 | 1 ⊢ (φ → (ψ → θ)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 176 |
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 |
This theorem is referenced by: 3imtr3d 258 ceqsalt 2882 sbceqal 3098 sbcimdv 3108 csbiebt 3173 rspcsbela 3196 ltfintri 4467 copsexg 4608 fce 6189 spacind 6288 |
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