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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.) |
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 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) | |
2 | pm3.31 461 | . 2 ⊢ ((𝜃 → (𝜏 → 𝜂)) → ((𝜃 ∧ 𝜏) → 𝜂)) | |
3 | 1, 2 | syl8 76 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → ((𝜃 ∧ 𝜏) → 𝜂)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 384 |
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 197 df-an 386 |
This theorem is referenced by: prtlem17 34161 tendospcanN 36312 |
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