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Mirrors > Home > MPE Home > Th. List > imp4c | 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 |
---|---|
imp4c | ⊢ (𝜑 → (((𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜏)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imp4.1 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) | |
2 | 1 | impd 396 | . 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜃 → 𝜏))) |
3 | 2 | impd 396 | 1 ⊢ (𝜑 → (((𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜏)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 382 |
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 383 |
This theorem is referenced by: imp44 415 imp5g 428 omordi 7800 omwordri 7806 omass 7814 oewordri 7826 umgrclwwlkge2 27141 upgr4cycl4dv4e 27365 elspansn5 28773 atcvat3i 29595 mdsymlem5 29606 sumdmdlem 29617 cvrat4 35251 sprsymrelfolem2 42271 |
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