Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE 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 9 | . 2 ⊢ (𝜑 → (𝜃 → (𝜒 → 𝜏))) |
4 | 1, 3 | syl5d 68 | 1 ⊢ (𝜑 → (𝜃 → (𝜓 → 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: syl9r 73 com23 78 sylan9 406 pm4.79dc 873 pclem6 1337 bilukdc 1359 sbequi 1795 reuss2 3326 reupick 3330 elres 4825 funimass4 5440 fliftfun 5665 elabgf2 12914 bj-rspgt 12920 |
Copyright terms: Public domain | W3C validator |