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Mirrors > Home > MPE Home > Th. List > imp45 | Structured version Visualization version GIF version |
Description: An importation inference. (Contributed by NM, 26-Apr-1994.) |
Ref | Expression |
---|---|
imp4.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
Ref | Expression |
---|---|
imp45 | ⊢ ((𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃))) → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imp4.1 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) | |
2 | 1 | imp4d 425 | . 2 ⊢ (𝜑 → ((𝜓 ∧ (𝜒 ∧ 𝜃)) → 𝜏)) |
3 | 2 | imp 407 | 1 ⊢ ((𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃))) → 𝜏) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 |
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 397 |
This theorem is referenced by: alexsubALTlem3 23198 spansncvi 30010 atcvatlem 30743 |
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