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| Mirrors > Home > MPE Home > Th. List > 3exp1 | Structured version Visualization version GIF version | ||
| Description: Exportation from left triple conjunction. (Contributed by NM, 24-Feb-2005.) |
| Ref | Expression |
|---|---|
| 3exp1.1 | ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜏) |
| Ref | Expression |
|---|---|
| 3exp1 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3exp1.1 | . . 3 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜏) | |
| 2 | 1 | ex 412 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 → 𝜏)) |
| 3 | 2 | 3exp 1120 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∧ wa 395 ∧ w3a 1087 |
| 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 207 df-an 396 df-3an 1089 |
| This theorem is referenced by: 3an1rs 1360 funelss 8072 ltmpi 10944 cshf1 14848 lcmfunsnlem 16678 mulgaddcom 19116 mulginvcom 19117 symgfvne 19398 voliunlem3 25587 3cyclfrgrrn 30305 numclwwlk1lem2foa 30373 frgrregord013 30414 strlem3a 32271 hstrlem3a 32279 chirredlem1 32409 nn0prpwlem 36323 matunitlindflem1 37623 zerdivemp1x 37954 athgt 39458 paddasslem14 39835 paddidm 39843 tendospcanN 41025 jm2.26 43014 relexpxpmin 43730 0ellimcdiv 45664 uhgrimisgrgric 47899 clnbgrgrimlem 47901 |
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