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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 421 | . 2 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏))) |
3 | 2 | exp4a 432 | 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: oaass 8044 zorn2lem4 9774 zorn2lem7 9777 iscatd2 16785 fgss2 22170 alexsubALTlem4 22346 grporcan 27982 spansncvi 29116 mdsymlem5 29871 riotasv3d 35648 cvratlem 36109 hbtlem2 39230 |
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