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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 1109 | 1 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜓) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 ∧ w3a 1086 |
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 1088 |
This theorem is referenced by: divcan7 11974 ccatrcan 14754 his7 31119 his2sub2 31122 hoadddir 31833 nndivsub 36440 rdgeqoa 37353 eel3132 44713 3impdirp1 44814 |
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