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Mirrors > Home > MPE Home > Th. List > 3mix1i | Structured version Visualization version GIF version |
Description: Introduction in triple disjunction. (Contributed by Mario Carneiro, 6-Oct-2014.) |
Ref | Expression |
---|---|
3mixi.1 | ⊢ 𝜑 |
Ref | Expression |
---|---|
3mix1i | ⊢ (𝜑 ∨ 𝜓 ∨ 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3mixi.1 | . 2 ⊢ 𝜑 | |
2 | 3mix1 1331 | . 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓 ∨ 𝜒)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜑 ∨ 𝜓 ∨ 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: ∨ w3o 1087 |
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 210 df-or 847 df-3or 1089 |
This theorem is referenced by: tpid1 4659 tpid1g 4660 0z 12073 ppiublem2 25939 |
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