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Mirrors > Home > MPE Home > Th. List > 3mix1d | Structured version Visualization version GIF version |
Description: Deduction introducing triple disjunction. (Contributed by Scott Fenton, 8-Jun-2011.) |
Ref | Expression |
---|---|
3mixd.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
3mix1d | ⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3mixd.1 | . 2 ⊢ (𝜑 → 𝜓) | |
2 | 3mix1 1223 | . 2 ⊢ (𝜓 → (𝜓 ∨ 𝜒 ∨ 𝜃)) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜃)) |
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: f1dom3fv3dif 6425 f1dom3el3dif 6426 elfiun 8219 lcmfunsnlem2lem2 15190 estrreslem2 16601 ostth 25128 btwncolg1 25250 hlln 25302 btwnlng1 25314 sltsolem1 31067 nodense 31088 colineartriv1 31344 fnwe2lem3 36640 prinfzo0 40363 |
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