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Mirrors > Home > MPE Home > Th. List > or12 | Structured version Visualization version GIF version |
Description: Swap two disjuncts. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 14-Nov-2012.) |
Ref | Expression |
---|---|
or12 | ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) ↔ (𝜓 ∨ (𝜑 ∨ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm1.5 544 | . 2 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) → (𝜓 ∨ (𝜑 ∨ 𝜒))) | |
2 | pm1.5 544 | . 2 ⊢ ((𝜓 ∨ (𝜑 ∨ 𝜒)) → (𝜑 ∨ (𝜓 ∨ 𝜒))) | |
3 | 1, 2 | impbii 199 | 1 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) ↔ (𝜓 ∨ (𝜑 ∨ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 196 ∨ wo 383 |
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 197 df-or 385 |
This theorem is referenced by: orass 546 or32 549 or4 550 3orcoma 1046 sotrieq 5062 ordzsl 7045 plydivex 24052 nosepon 31818 |
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