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Theorem exp4d 361
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
exp4d.1 (𝜑 → ((𝜓 ∧ (𝜒𝜃)) → 𝜏))
Assertion
Ref Expression
exp4d (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))

Proof of Theorem exp4d
StepHypRef Expression
1 exp4d.1 . . 3 (𝜑 → ((𝜓 ∧ (𝜒𝜃)) → 𝜏))
21expd 254 . 2 (𝜑 → (𝜓 → ((𝜒𝜃) → 𝜏)))
32exp4a 358 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  tfrlem9  5968  facdiv  9762
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