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Theorem 3exp2 1161
Description: Exportation from right triple conjunction. (Contributed by NM, 26-Oct-2006.)
Hypothesis
Ref Expression
3exp2.1 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)
Assertion
Ref Expression
3exp2 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))

Proof of Theorem 3exp2
StepHypRef Expression
1 3exp2.1 . . 3 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)
21ex 113 . 2 (𝜑 → ((𝜓𝜒𝜃) → 𝜏))
323expd 1160 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 924
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  df-3an 926
This theorem is referenced by:  3anassrs  1165  po2nr  4127  fliftfund  5558  tfrlemibxssdm  6074  tfr1onlembxssdm  6090  tfrcllembxssdm  6103
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