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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 sbi1OLD 2519 sbi1ALT 2582 mopick 2687 isofrlem 7072 kmlem9 9569 squeeze0 11532 lcmfunsnlem1 15971 fgss2 22479 ordcmp 33908 linepsubN 37048 pmapsub 37064 ichreuopeq 43990 bgoldbnnsum3prm 44322 |
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