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Mirrors > Home > MPE Home > Th. List > imp5a | Structured version Visualization version GIF version |
Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009.) (Proof shortened by Wolf Lammen, 2-Aug-2022.) |
Ref | Expression |
---|---|
imp5.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) |
Ref | Expression |
---|---|
imp5a | ⊢ (𝜑 → (𝜓 → (𝜒 → ((𝜃 ∧ 𝜏) → 𝜂)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imp5.1 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) | |
2 | 1 | imp5d 443 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → ((𝜃 ∧ 𝜏) → 𝜂)) |
3 | 2 | exp31 423 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → ((𝜃 ∧ 𝜏) → 𝜂)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 |
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 210 df-an 400 |
This theorem is referenced by: prtlem17 36545 tendospcanN 38692 |
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