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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 419 | . 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜃 → 𝜏))) |
3 | 2 | expd 415 | 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: isofrlem 7359 f1ocnv2d 7685 oelim 8570 zorn2lem7 10539 addrid 11438 initoeu1 18064 termoeu1 18071 issubg4 19175 lmodvsdir 20900 lmodvsass 20901 gsummatr01lem4 22679 dvfsumrlim3 26088 wwlksext2clwwlk 30085 shscli 31345 f1o3d 32643 slmdvsdir 33204 slmdvsass 33205 lshpcmp 38969 |
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