![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > 3orel2OLD | Structured version Visualization version GIF version |
Description: Obsolete version of 3orel2 1483 as of 8-Oct-2025. (Contributed by Scott Fenton, 26-Mar-2011.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
3orel2OLD | ⊢ (¬ 𝜓 → ((𝜑 ∨ 𝜓 ∨ 𝜒) → (𝜑 ∨ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3orrot 1091 | . 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒 ∨ 𝜑)) | |
2 | 3orel1 1090 | . . 3 ⊢ (¬ 𝜓 → ((𝜓 ∨ 𝜒 ∨ 𝜑) → (𝜒 ∨ 𝜑))) | |
3 | orcom 870 | . . 3 ⊢ ((𝜒 ∨ 𝜑) ↔ (𝜑 ∨ 𝜒)) | |
4 | 2, 3 | imbitrdi 251 | . 2 ⊢ (¬ 𝜓 → ((𝜓 ∨ 𝜒 ∨ 𝜑) → (𝜑 ∨ 𝜒))) |
5 | 1, 4 | biimtrid 242 | 1 ⊢ (¬ 𝜓 → ((𝜑 ∨ 𝜓 ∨ 𝜒) → (𝜑 ∨ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 847 ∨ w3o 1085 |
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 207 df-or 848 df-3or 1087 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |