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Mirrors > Home > MPE Home > Th. List > 3mix2d | 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 |
---|---|
3mix2d | ⊢ (𝜑 → (𝜒 ∨ 𝜓 ∨ 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3mixd.1 | . 2 ⊢ (𝜑 → 𝜓) | |
2 | 3mix2 1416 | . 2 ⊢ (𝜓 → (𝜒 ∨ 𝜓 ∨ 𝜃)) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝜒 ∨ 𝜓 ∨ 𝜃)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ w3o 1071 |
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 197 df-or 384 df-3or 1073 |
This theorem is referenced by: sosn 5345 funtpgOLD 6104 f1dom3fv3dif 6688 f1dom3el3dif 6689 elfiun 8501 fpwwe2lem13 9656 lcmfunsnlem2lem2 15554 dyaddisjlem 23563 tgcolg 25648 btwncolg2 25650 hlln 25701 btwnlng2 25714 frgrregorufr0 27478 sltsolem1 32132 colineartriv2 32481 |
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