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Mirrors > Home > ILE Home > Th. List > 3mix2 | 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 1167 | . 2 ⊢ (𝜑 → (𝜑 ∨ 𝜒 ∨ 𝜓)) | |
2 | 3orrot 985 | . 2 ⊢ ((𝜓 ∨ 𝜑 ∨ 𝜒) ↔ (𝜑 ∨ 𝜒 ∨ 𝜓)) | |
3 | 1, 2 | sylibr 134 | 1 ⊢ (𝜑 → (𝜓 ∨ 𝜑 ∨ 𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ w3o 978 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 |
This theorem depends on definitions: df-bi 117 df-3or 980 |
This theorem is referenced by: 3mix2i 1171 3mix2d 1174 3jaob 1312 funtpg 5279 elnn0z 9280 nn0le2is012 9349 nn01to3 9631 zabsle1 14753 triap 15131 |
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