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Theorem exp42 437
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 421 . 2 (𝜑 → ((𝜓𝜒) → (𝜃𝜏)))
32expd 417 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397
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 398
This theorem is referenced by:  isofrlem  7337  f1ocnv2d  7659  oelim  8534  zorn2lem7  10497  addrid  11394  initoeu1  17961  termoeu1  17968  issubg4  19025  lmodvsdir  20496  lmodvsass  20497  gsummatr01lem4  22160  dvfsumrlim3  25550  wwlksext2clwwlk  29310  shscli  30570  f1o3d  31851  slmdvsdir  32361  slmdvsass  32362  lshpcmp  37858
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