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Mirrors > Home > ILE Home > Th. List > 3orrot | GIF version |
Description: Rotation law for triple disjunction. (Contributed by NM, 4-Apr-1995.) |
Ref | Expression |
---|---|
3orrot | ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒 ∨ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orcom 647 | . 2 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) ↔ ((𝜓 ∨ 𝜒) ∨ 𝜑)) | |
2 | 3orass 888 | . 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒))) | |
3 | df-3or 886 | . 2 ⊢ ((𝜓 ∨ 𝜒 ∨ 𝜑) ↔ ((𝜓 ∨ 𝜒) ∨ 𝜑)) | |
4 | 1, 2, 3 | 3bitr4i 201 | 1 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒 ∨ 𝜑)) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 98 ∨ wo 629 ∨ w3o 884 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 |
This theorem depends on definitions: df-bi 110 df-3or 886 |
This theorem is referenced by: 3mix2 1074 3mix3 1075 eueq3dc 2715 tprot 3463 sotritrieq 4062 elnnz 8255 elznn 8261 ztri3or0 8287 zapne 8315 |
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