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Theorem imp42 426
Description: An importation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
imp4.1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Assertion
Ref Expression
imp42 (((𝜑 ∧ (𝜓𝜒)) ∧ 𝜃) → 𝜏)

Proof of Theorem imp42
StepHypRef Expression
1 imp4.1 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
21imp32 418 . 2 ((𝜑 ∧ (𝜓𝜒)) → (𝜃𝜏))
32imp 406 1 (((𝜑 ∧ (𝜓𝜒)) ∧ 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:  imp55  442  ltexprlem7  11082  fzdif1  13645  iscatd  17716  isposd  18368  pospropd  18372  mulgghm2  21487  ordtbaslem  23196  txbas  23575  nocvxminlem  27822  frgrncvvdeqlem8  30325  grporcan  30537  chirredlem1  32409  cvxpconn  35247  cvxsconn  35248  rngonegmn1l  37948  prnc  38074  reuopreuprim  47513  uhgrimisgrgriclem  47898
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