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Theorem exp42 357
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 350 . 2 (𝜑 → ((𝜓𝜒) → (𝜃𝜏)))
32expd 249 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 105
This theorem is referenced by:  f1ocnv2d  5732
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