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Mirrors > Home > ILE Home > Th. List > or32 | GIF version |
Description: A rearrangement of disjuncts. (Contributed by NM, 18-Oct-1995.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
or32 | ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ ((𝜑 ∨ 𝜒) ∨ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orass 762 | . 2 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒))) | |
2 | or12 761 | . 2 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) ↔ (𝜓 ∨ (𝜑 ∨ 𝜒))) | |
3 | orcom 723 | . 2 ⊢ ((𝜓 ∨ (𝜑 ∨ 𝜒)) ↔ ((𝜑 ∨ 𝜒) ∨ 𝜓)) | |
4 | 1, 2, 3 | 3bitri 205 | 1 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ ((𝜑 ∨ 𝜒) ∨ 𝜓)) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 104 ∨ wo 703 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: xrnepnf 9724 |
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