Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > pm1.5 | GIF version |
Description: Axiom *1.5 (Assoc) of [WhiteheadRussell] p. 96. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm1.5 | ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) → (𝜓 ∨ (𝜑 ∨ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 665 | . . 3 ⊢ (𝜑 → (𝜑 ∨ 𝜒)) | |
2 | 1 | olcd 685 | . 2 ⊢ (𝜑 → (𝜓 ∨ (𝜑 ∨ 𝜒))) |
3 | olc 664 | . . 3 ⊢ (𝜒 → (𝜑 ∨ 𝜒)) | |
4 | 3 | orim2i 710 | . 2 ⊢ ((𝜓 ∨ 𝜒) → (𝜓 ∨ (𝜑 ∨ 𝜒))) |
5 | 2, 4 | jaoi 668 | 1 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) → (𝜓 ∨ (𝜑 ∨ 𝜒))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ wo 661 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: or12 715 |
Copyright terms: Public domain | W3C validator |