Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > 3mix3 | GIF version |
Description: Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.) |
Ref | Expression |
---|---|
3mix3 | ⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3mix1 1155 | . 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓 ∨ 𝜒)) | |
2 | 3orrot 973 | . 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒 ∨ 𝜑)) | |
3 | 1, 2 | sylib 121 | 1 ⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜑)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ w3o 966 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 |
This theorem depends on definitions: df-bi 116 df-3or 968 |
This theorem is referenced by: 3mix3i 1160 3mix3d 1163 3jaob 1291 tpid3g 3686 funtpg 5234 exmidontriimlem3 7171 nn0le2is012 9265 nn01to3 9547 fztri3or 9965 qbtwnxr 10184 hashfiv01gt1 10685 |
Copyright terms: Public domain | W3C validator |