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| Mirrors > Home > MPE Home > Th. List > exp4d | Structured version Visualization version GIF version | ||
| Description: An exportation inference. (Contributed by NM, 26-Apr-1994.) |
| Ref | Expression |
|---|---|
| exp4d.1 | ⊢ (𝜑 → ((𝜓 ∧ (𝜒 ∧ 𝜃)) → 𝜏)) |
| Ref | Expression |
|---|---|
| exp4d | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | exp4d.1 | . . 3 ⊢ (𝜑 → ((𝜓 ∧ (𝜒 ∧ 𝜃)) → 𝜏)) | |
| 2 | 1 | expd 415 | . 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: tfrlem9 8425 omass 8618 pssnn 9208 cardinfima 10137 ltexprlem7 11082 facdiv 14326 infpnlem1 16948 atcvatlem 32404 mdsymlem5 32426 mdsymlem7 32428 btwnconn1lem11 36098 exp5k 36305 |
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