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Theorem imp42 427
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 419 . 2 ((𝜑 ∧ (𝜓𝜒)) → (𝜃𝜏))
32imp 407 1 (((𝜑 ∧ (𝜓𝜒)) ∧ 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  11019  iscatd  17599  isposd  18258  pospropd  18262  mulgghm2  20979  ordtbaslem  22621  txbas  23000  nocvxminlem  27205  frgrncvvdeqlem8  29424  grporcan  29634  chirredlem1  31506  cvxpconn  34064  cvxsconn  34065  rngonegmn1l  36614  prnc  36740  reuopreuprim  45966
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