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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 418 | . 2 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏))) |
3 | 2 | exp4a 434 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 398 |
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 209 df-an 399 |
This theorem is referenced by: tfrlem9 8020 omass 8205 pssnn 8735 cardinfima 9522 ltexprlem7 10463 facdiv 13646 infpnlem1 16245 atcvatlem 30161 mdsymlem5 30183 mdsymlem7 30185 btwnconn1lem11 33558 exp5k 33652 |
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