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Theorem exp41 370
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
exp41.1 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)
Assertion
Ref Expression
exp41 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))

Proof of Theorem exp41
StepHypRef Expression
1 exp41.1 . . 3 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)
21ex 115 . 2 (((𝜑𝜓) ∧ 𝜒) → (𝜃𝜏))
32exp31 364 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108
This theorem is referenced by:  apexp1  10669
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