Theorem 3exp2 1215

Description: Exportation from right triple conjunction. (Contributed by NM, 26-Oct-2006.)

Hypothesis

Ref	Expression
3exp2.1	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) → 𝜏)

Assertion

Ref	Expression
3exp2	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Proof of Theorem 3exp2

Step	Hyp	Ref	Expression
1		3exp2.1	. . 3 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) → 𝜏)
2	1	ex 114	. 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏))
3	2	3expd 1214	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Syntax hints:   → wi 4   ∧ wa 103   ∧ w3a 968

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 970

This theorem is referenced by:  3anassrs  1219  po2nr  4287  fliftfund  5765  tfrlemibxssdm  6295  tfr1onlembxssdm  6311  tfrcllembxssdm  6324  isxmetd  12987  dvidlemap  13300