Theorem exp5o 1157

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 254	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 → (𝜏 → 𝜂)))
3	2	3exp 1137	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Syntax hints:   → wi 4   ∧ wa 102   ∧ w3a 919

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 921

This theorem is referenced by:  exp520  1159  bndndx  8287