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| Mirrors > Home > MPE Home > Th. List > exp45 | Structured version Visualization version GIF version | ||
| Description: An exportation inference. (Contributed by NM, 26-Apr-1994.) | 
| Ref | Expression | 
|---|---|
| exp45.1 | ⊢ ((𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃))) → 𝜏) | 
| Ref | Expression | 
|---|---|
| exp45 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | exp45.1 | . . 3 ⊢ ((𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃))) → 𝜏) | |
| 2 | 1 | exp32 420 | . 2 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏))) | 
| 3 | 2 | exp4a 431 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∧ wa 395 | 
| 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 207 df-an 396 | 
| This theorem is referenced by: oaass 8600 zorn2lem4 10540 zorn2lem7 10543 iscatd2 17725 fgss2 23883 alexsubALTlem4 24059 grporcan 30538 spansncvi 31672 mdsymlem5 32427 riotasv3d 38962 cvratlem 39424 hbtlem2 43141 | 
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