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Mirrors > Home > MPE Home > Th. List > orordir | Structured version Visualization version GIF version |
Description: Distribution of disjunction over disjunction. (Contributed by NM, 25-Feb-1995.) |
Ref | Expression |
---|---|
orordir | ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ ((𝜑 ∨ 𝜒) ∨ (𝜓 ∨ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oridm 904 | . . 3 ⊢ ((𝜒 ∨ 𝜒) ↔ 𝜒) | |
2 | 1 | orbi2i 912 | . 2 ⊢ (((𝜑 ∨ 𝜓) ∨ (𝜒 ∨ 𝜒)) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒)) |
3 | or4 926 | . 2 ⊢ (((𝜑 ∨ 𝜓) ∨ (𝜒 ∨ 𝜒)) ↔ ((𝜑 ∨ 𝜒) ∨ (𝜓 ∨ 𝜒))) | |
4 | 2, 3 | bitr3i 277 | 1 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ ((𝜑 ∨ 𝜒) ∨ (𝜓 ∨ 𝜒))) |
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: sspsstri 4067 psslinpr 10974 elznn0 12521 tosso 18315 legso 27583 |
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