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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 8544 omcan 8565 ecovdi 8815 distrpi 10889 axltadd 11283 ccatlcan 14664 absmulgcd 16487 axlowdimlem14 28193 fh1 30849 fh2 30850 cm2j 30851 hoadddi 31034 hosubdi 31039 leopmul2i 31366 dvconstbi 43026 eel2131 43408 uun2131 43485 uun2131p1 43486 io1ii 47455 reccot 47705 rectan 47706 |
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