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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 411 | . 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜃 → 𝜏))) |
3 | 2 | impd 411 | 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 208 df-an 397 |
This theorem is referenced by: imp44 429 reuop 6137 omordi 8181 omwordri 8187 omass 8195 oewordri 8207 umgrclwwlkge2 27696 upgr4cycl4dv4e 27891 elspansn5 29278 atcvat3i 30100 mdsymlem5 30111 sumdmdlem 30122 cvrat4 36459 2reuimp 43191 sprsymrelfolem2 43532 reupr 43561 |
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