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Mirrors > Home > ILE Home > Th. List > imp4d | GIF version |
Description: An importation inference. (Contributed by NM, 26-Apr-1994.) |
Ref | Expression |
---|---|
imp4.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
Ref | Expression |
---|---|
imp4d | ⊢ (𝜑 → ((𝜓 ∧ (𝜒 ∧ 𝜃)) → 𝜏)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imp4.1 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) | |
2 | 1 | imp4a 349 | . 2 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏))) |
3 | 2 | impd 254 | 1 ⊢ (𝜑 → ((𝜓 ∧ (𝜒 ∧ 𝜃)) → 𝜏)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: imp45 357 tfrlem9 6314 uzind 9350 facdiv 10699 |
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