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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 870 | . 2 ⊢ (((𝜑 ∧ 𝜒) ∧ 𝜓) → 𝜃) |
3 | 2 | 3impa 1251 | 1 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜓) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∧ w3a 1031 |
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-an 385 df-3an 1033 |
This theorem is referenced by: divcan7 10613 ccatrcan 13325 his7 27331 his2sub2 27334 hoadddir 28047 nndivsub 31626 rdgeqoa 32394 eel3132 37961 3impdirp1 38064 |
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