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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 674 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) |
3 | 2 | 3impb 1108 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 ∧ w3a 1080 |
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 208 df-an 397 df-3an 1082 |
This theorem is referenced by: oacan 8031 omcan 8052 ecovdi 8262 distrpi 10173 axltadd 10567 ccatlcan 13920 absmulgcd 15730 axlowdimlem14 26428 fh1 29082 fh2 29083 cm2j 29084 hoadddi 29267 hosubdi 29272 leopmul2i 29599 dvconstbi 40225 eel2131 40608 uun2131 40685 uun2131p1 40686 reccot 44359 rectan 44360 |
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