![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > or4 | Structured version Visualization version GIF version |
Description: Rearrangement of 4 disjuncts. (Contributed by NM, 12-Aug-1994.) |
Ref | Expression |
---|---|
or4 | ⊢ (((𝜑 ∨ 𝜓) ∨ (𝜒 ∨ 𝜃)) ↔ ((𝜑 ∨ 𝜒) ∨ (𝜓 ∨ 𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | or12 920 | . . 3 ⊢ ((𝜓 ∨ (𝜒 ∨ 𝜃)) ↔ (𝜒 ∨ (𝜓 ∨ 𝜃))) | |
2 | 1 | orbi2i 912 | . 2 ⊢ ((𝜑 ∨ (𝜓 ∨ (𝜒 ∨ 𝜃))) ↔ (𝜑 ∨ (𝜒 ∨ (𝜓 ∨ 𝜃)))) |
3 | orass 921 | . 2 ⊢ (((𝜑 ∨ 𝜓) ∨ (𝜒 ∨ 𝜃)) ↔ (𝜑 ∨ (𝜓 ∨ (𝜒 ∨ 𝜃)))) | |
4 | orass 921 | . 2 ⊢ (((𝜑 ∨ 𝜒) ∨ (𝜓 ∨ 𝜃)) ↔ (𝜑 ∨ (𝜒 ∨ (𝜓 ∨ 𝜃)))) | |
5 | 2, 3, 4 | 3bitr4i 303 | 1 ⊢ (((𝜑 ∨ 𝜓) ∨ (𝜒 ∨ 𝜃)) ↔ ((𝜑 ∨ 𝜒) ∨ (𝜓 ∨ 𝜃))) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∨ wo 846 |
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 847 |
This theorem is referenced by: or42 927 orordi 928 orordir 929 3or6 1448 swoer 8685 xmullem2 13191 swrdnnn0nd 14551 clsk1indlem3 42389 |
Copyright terms: Public domain | W3C validator |