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| Mirrors > Home > MPE Home > Th. List > 3impdir | Structured version Visualization version GIF version | ||
| Description: Importation inference (undistribute conjunction). (Contributed by NM, 20-Aug-1995.) |
| Ref | Expression |
|---|---|
| 3impdir.1 | ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜓)) → 𝜃) |
| Ref | Expression |
|---|---|
| 3impdir | ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜓) → 𝜃) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3impdir.1 | . . 3 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜓)) → 𝜃) | |
| 2 | 1 | anandirs 679 | . 2 ⊢ (((𝜑 ∧ 𝜒) ∧ 𝜓) → 𝜃) |
| 3 | 2 | 3impa 1110 | 1 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜓) → 𝜃) |
| 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: divcan7 11976 ccatrcan 14757 his7 31109 his2sub2 31112 hoadddir 31823 nndivsub 36458 rdgeqoa 37371 eel3132 44735 3impdirp1 44836 |
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