![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > or32 | Structured version Visualization version GIF version |
Description: A rearrangement of disjuncts. (Contributed by NM, 18-Oct-1995.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
or32 | ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ ((𝜑 ∨ 𝜒) ∨ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orass 920 | . 2 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒))) | |
2 | or12 919 | . 2 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) ↔ (𝜓 ∨ (𝜑 ∨ 𝜒))) | |
3 | orcom 868 | . 2 ⊢ ((𝜓 ∨ (𝜑 ∨ 𝜒)) ↔ ((𝜑 ∨ 𝜒) ∨ 𝜓)) | |
4 | 1, 2, 3 | 3bitri 296 | 1 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ ((𝜑 ∨ 𝜒) ∨ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∨ wo 845 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 df-or 846 |
This theorem is referenced by: sspsstri 4101 somo 5624 psslinpr 11022 xrnepnf 13094 xrinfmss 13285 tosso 18368 mulsproplem13 27573 mulsproplem14 27574 satfvsucsuc 34344 lineunray 35107 or32dd 36950 |
Copyright terms: Public domain | W3C validator |