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Mirrors > Home > MPE Home > Th. List > 3impdi | Structured version Visualization version GIF version |
Description: Importation inference (undistribute conjunction). (Contributed by NM, 14-Aug-1995.) |
Ref | Expression |
---|---|
3impdi.1 | ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜑 ∧ 𝜒)) → 𝜃) |
Ref | Expression |
---|---|
3impdi | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3impdi.1 | . . 3 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜑 ∧ 𝜒)) → 𝜃) | |
2 | 1 | anandis 677 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) |
3 | 2 | 3impb 1116 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 397 ∧ w3a 1088 |
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 206 df-an 398 df-3an 1090 |
This theorem is referenced by: oacan 8548 omcan 8569 ecovdi 8819 distrpi 10893 axltadd 11287 ccatlcan 14668 absmulgcd 16491 axlowdimlem14 28213 fh1 30871 fh2 30872 cm2j 30873 hoadddi 31056 hosubdi 31061 leopmul2i 31388 dvconstbi 43093 eel2131 43475 uun2131 43552 uun2131p1 43553 io1ii 47553 reccot 47803 rectan 47804 |
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