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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 419 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → (𝜃 → 𝜏)) |
3 | 2 | imp 407 | 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 206 df-an 397 |
This theorem is referenced by: imp55 443 ltexprlem7 11033 iscatd 17613 isposd 18272 pospropd 18276 mulgghm2 21037 ordtbaslem 22683 txbas 23062 nocvxminlem 27268 frgrncvvdeqlem8 29548 grporcan 29758 chirredlem1 31630 cvxpconn 34221 cvxsconn 34222 rngonegmn1l 36797 prnc 36923 reuopreuprim 46180 |
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