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Mirrors > Home > MPE Home > Th. List > imp42 | Structured version Visualization version GIF version |
Description: An importation inference. (Contributed by NM, 26-Apr-1994.) |
Ref | Expression |
---|---|
imp4.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
Ref | Expression |
---|---|
imp42 | ⊢ (((𝜑 ∧ (𝜓 ∧ 𝜒)) ∧ 𝜃) → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imp4.1 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) | |
2 | 1 | imp32 422 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → (𝜃 → 𝜏)) |
3 | 2 | imp 410 | 1 ⊢ (((𝜑 ∧ (𝜓 ∧ 𝜒)) ∧ 𝜃) → 𝜏) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 |
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 210 df-an 400 |
This theorem is referenced by: imp55 446 ltexprlem7 10656 iscatd 17176 isposd 17830 pospropd 17833 mulgghm2 20463 ordtbaslem 22085 txbas 22464 frgrncvvdeqlem8 28389 grporcan 28599 chirredlem1 30471 cvxpconn 32917 cvxsconn 32918 nocvxminlem 33709 rngonegmn1l 35836 prnc 35962 reuopreuprim 44651 |
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