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Mirrors > Home > NFE Home > Th. List > syl9 | GIF version |
Description: A nested syllogism inference with different antecedents. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.) |
Ref | Expression |
---|---|
syl9.1 | ⊢ (φ → (ψ → χ)) |
syl9.2 | ⊢ (θ → (χ → τ)) |
Ref | Expression |
---|---|
syl9 | ⊢ (φ → (θ → (ψ → τ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl9.1 | . 2 ⊢ (φ → (ψ → χ)) | |
2 | syl9.2 | . . 3 ⊢ (θ → (χ → τ)) | |
3 | 2 | a1i 10 | . 2 ⊢ (φ → (θ → (χ → τ))) |
4 | 1, 3 | syl5d 62 | 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: syl9r 67 com23 72 sylan9 638 19.21t 1795 19.21tOLD 1863 sbequi 2059 sbal1 2126 reuss2 3535 reupick 3539 ssfin 4470 iss 5000 |
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