![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > orim1d | GIF version |
Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.) |
Ref | Expression |
---|---|
orim1d.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
orim1d | ⊢ (𝜑 → ((𝜓 ∨ 𝜃) → (𝜒 ∨ 𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orim1d.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | idd 21 | . 2 ⊢ (𝜑 → (𝜃 → 𝜃)) | |
3 | 1, 2 | orim12d 736 | 1 ⊢ (𝜑 → ((𝜓 ∨ 𝜃) → (𝜒 ∨ 𝜃))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ wo 665 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: pm2.38 753 pm2.73 756 pm2.74 757 pm2.8 760 pm2.82 762 unss1 3170 acexmidlemcase 5661 exmidomniim 6858 nn0ge2m1nn 8794 exmidsbthrlem 12184 |
Copyright terms: Public domain | W3C validator |