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Mirrors > Home > MPE Home > Th. List > syl5d | Structured version Visualization version GIF version |
Description: A nested syllogism deduction. Deduction associated with syl5 34. (Contributed by NM, 14-May-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.) (Proof shortened by Mel L. O'Cat, 2-Feb-2006.) |
Ref | Expression |
---|---|
syl5d.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
syl5d.2 | ⊢ (𝜑 → (𝜃 → (𝜒 → 𝜏))) |
Ref | Expression |
---|---|
syl5d | ⊢ (𝜑 → (𝜃 → (𝜓 → 𝜏))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl5d.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | 1 | a1d 25 | . 2 ⊢ (𝜑 → (𝜃 → (𝜓 → 𝜒))) |
3 | syl5d.2 | . 2 ⊢ (𝜑 → (𝜃 → (𝜒 → 𝜏))) | |
4 | 2, 3 | syldd 72 | 1 ⊢ (𝜑 → (𝜃 → (𝜓 → 𝜏))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: syl7 74 syl9 77 imim12d 81 mopick 2617 isofrlem 7348 kmlem9 10181 squeeze0 12147 lcmfunsnlem1 16607 rnglidlmcl 21111 fgss2 23777 ordcmp 35931 linepsubN 39225 pmapsub 39241 ichreuopeq 46813 bgoldbnnsum3prm 47144 |
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