Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > imim12d | GIF version |
Description: Deduction combining antecedents and consequents. (Contributed by NM, 7-Aug-1994.) (Proof shortened by O'Cat, 30-Oct-2011.) |
Ref | Expression |
---|---|
imim12d.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
imim12d.2 | ⊢ (𝜑 → (𝜃 → 𝜏)) |
Ref | Expression |
---|---|
imim12d | ⊢ (𝜑 → ((𝜒 → 𝜃) → (𝜓 → 𝜏))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imim12d.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | imim12d.2 | . . 3 ⊢ (𝜑 → (𝜃 → 𝜏)) | |
3 | 2 | imim2d 54 | . 2 ⊢ (𝜑 → ((𝜒 → 𝜃) → (𝜒 → 𝜏))) |
4 | 1, 3 | syl5d 68 | 1 ⊢ (𝜑 → ((𝜒 → 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: imim1d 75 equveli 1752 hbsb4t 2006 mo23 2060 rspcimdv 2835 r19.29uz 10956 txlm 13073 metcnpi3 13311 addcncntoplem 13345 cnplimcim 13430 setindis 14002 bdsetindis 14004 bj-findis 14014 |
Copyright terms: Public domain | W3C validator |