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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 422 | . 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜃 → 𝜏))) |
3 | 2 | expd 418 | 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: isofrlem 7093 f1ocnv2d 7398 oelim 8159 zorn2lem7 9924 addid1 10820 initoeu1 17271 termoeu1 17278 issubg4 18298 lmodvsdir 19658 lmodvsass 19659 gsummatr01lem4 21267 dvfsumrlim3 24630 wwlksext2clwwlk 27836 shscli 29094 f1o3d 30372 slmdvsdir 30844 slmdvsass 30845 lshpcmp 36139 |
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