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Theorem exp42 435
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
exp42.1 (((𝜑 ∧ (𝜓𝜒)) ∧ 𝜃) → 𝜏)
Assertion
Ref Expression
exp42 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))

Proof of Theorem exp42
StepHypRef Expression
1 exp42.1 . . 3 (((𝜑 ∧ (𝜓𝜒)) ∧ 𝜃) → 𝜏)
21exp31 419 . 2 (𝜑 → ((𝜓𝜒) → (𝜃𝜏)))
32expd 415 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
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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