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Mirrors > Home > MPE Home > Th. List > exp42 | Structured version Visualization version GIF version |
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.) |
Ref | Expression |
---|---|
exp42.1 | ⊢ (((𝜑 ∧ (𝜓 ∧ 𝜒)) ∧ 𝜃) → 𝜏) |
Ref | Expression |
---|---|
exp42 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exp42.1 | . . 3 ⊢ (((𝜑 ∧ (𝜓 ∧ 𝜒)) ∧ 𝜃) → 𝜏) | |
2 | 1 | exp31 628 | . 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜃 → 𝜏))) |
3 | 2 | expd 451 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 |
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 196 df-an 385 |
This theorem is referenced by: isofrlem 6490 f1ocnv2d 6784 oelim 7501 zorn2lem7 9207 addid1 10095 initoeu1 16484 termoeu1 16491 issubg4 17436 lmodvsdir 18710 lmodvsass 18711 gsummatr01lem4 20283 dvfsumrlim3 23600 shscli 27560 f1o3d 28813 slmdvsdir 29100 slmdvsass 29101 lshpcmp 33293 |
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