Theorem exp5o 1221

Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Hypothesis

Ref	Expression
exp5o.1	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → ((𝜃 ∧ 𝜏) → 𝜂))

Assertion

Ref	Expression
exp5o	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Proof of Theorem exp5o

Step	Hyp	Ref	Expression
1		exp5o.1	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → ((𝜃 ∧ 𝜏) → 𝜂))
2	1	expd 256	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 → (𝜏 → 𝜂)))
3	2	3exp 1197	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Syntax hints:   → wi 4   ∧ wa 103   ∧ w3a 973

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 975

This theorem is referenced by:  exp520  1223  bndndx  9134