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Mirrors > Home > NFE Home > Th. List > syl5d | 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.) |
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 22 | . 2 ⊢ (φ → (θ → (ψ → χ))) |
3 | syl5d.2 | . 2 ⊢ (φ → (θ → (χ → τ))) | |
4 | 2, 3 | syldd 61 | 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 63 syl9 66 imim12d 68 sbi1 2063 |
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