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Theorem 3exp2 1188
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 114 . 2 (𝜑 → ((𝜓𝜒𝜃) → 𝜏))
323expd 1187 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 949
This theorem is referenced by:  3anassrs  1192  po2nr  4201  fliftfund  5666  tfrlemibxssdm  6192  tfr1onlembxssdm  6208  tfrcllembxssdm  6221  isxmetd  12443  dvidlemap  12756
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