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Mirrors > Home > ILE Home > Th. List > 3mix1i | 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 1115 | . 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓 ∨ 𝜒)) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ (𝜑 ∨ 𝜓 ∨ 𝜒) |
Colors of variables: wff set class |
Syntax hints: ∨ w3o 926 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 668 |
This theorem depends on definitions: df-bi 116 df-3or 928 |
This theorem is referenced by: tpid1 3573 tpid1g 3574 0z 8859 |
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