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Mirrors > Home > ILE Home > Th. List > syl6d | GIF version |
Description: A nested syllogism deduction. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.) (Proof shortened by O'Cat, 2-Feb-2006.) (Revised by NM, 3-Feb-2006.) |
Ref | Expression |
---|---|
syl6d.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
syl6d.2 | ⊢ (𝜑 → (𝜃 → 𝜏)) |
Ref | Expression |
---|---|
syl6d | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl6d.1 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
2 | syl6d.2 | . . 3 ⊢ (𝜑 → (𝜃 → 𝜏)) | |
3 | 2 | a1d 22 | . 2 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜏))) |
4 | 1, 3 | syldd 67 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏))) |
Colors of variables: wff set 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: syl8 71 |
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