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Mirrors > Home > ILE Home > Th. List > 3mix3 | GIF version |
Description: Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.) |
Ref | Expression |
---|---|
3mix3 | ⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3mix1 1073 | . 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓 ∨ 𝜒)) | |
2 | 3orrot 891 | . 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒 ∨ 𝜑)) | |
3 | 1, 2 | sylib 127 | 1 ⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜑)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ w3o 884 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 |
This theorem depends on definitions: df-bi 110 df-3or 886 |
This theorem is referenced by: 3mix3i 1078 3mix3d 1081 3jaob 1197 tpid3g 3483 funtpg 4950 nn01to3 8552 fztri3or 8903 |
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