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Mirrors > Home > MPE Home > Th. List > 3mix2 | Structured version Visualization version GIF version |
Description: Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.) |
Ref | Expression |
---|---|
3mix2 | ⊢ (𝜑 → (𝜓 ∨ 𝜑 ∨ 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3mix1 1223 | . 2 ⊢ (𝜑 → (𝜑 ∨ 𝜒 ∨ 𝜓)) | |
2 | 3orrot 1037 | . 2 ⊢ ((𝜓 ∨ 𝜑 ∨ 𝜒) ↔ (𝜑 ∨ 𝜒 ∨ 𝜓)) | |
3 | 1, 2 | sylibr 223 | 1 ⊢ (𝜑 → (𝜓 ∨ 𝜑 ∨ 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ w3o 1030 |
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 df-3or 1032 |
This theorem is referenced by: 3mix2i 1227 3mix2d 1230 3jaob 1382 tppreqb 4277 tpres 6371 onzsl 6938 sornom 8982 hash1to3 13128 cshwshashlem1 15640 zabsle1 24821 ostth 25128 sltsolem1 31067 nodenselem8 31087 fnwe2lem3 36640 nn0le2is012 41938 |
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