Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > pm2.41 | Structured version Visualization version GIF version |
Description: Theorem *2.41 of [WhiteheadRussell] p. 106. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm2.41 | ⊢ ((𝜓 ∨ (𝜑 ∨ 𝜓)) → (𝜑 ∨ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | olc 398 | . 2 ⊢ (𝜓 → (𝜑 ∨ 𝜓)) | |
2 | id 22 | . 2 ⊢ ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜓)) | |
3 | 1, 2 | jaoi 393 | 1 ⊢ ((𝜓 ∨ (𝜑 ∨ 𝜓)) → (𝜑 ∨ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 382 |
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 196 df-or 384 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |