Theorem exp511 33651

Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)

Hypothesis

Ref	Expression
exp511.1	⊢ ((𝜑 ∧ ((𝜓 ∧ (𝜒 ∧ 𝜃)) ∧ 𝜏)) → 𝜂)

Assertion

Ref	Expression
exp511	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Proof of Theorem exp511

Step	Hyp	Ref	Expression
1		exp511.1	. . 3 ⊢ ((𝜑 ∧ ((𝜓 ∧ (𝜒 ∧ 𝜃)) ∧ 𝜏)) → 𝜂)
2	1	ex 415	. 2 ⊢ (𝜑 → (((𝜓 ∧ (𝜒 ∧ 𝜃)) ∧ 𝜏) → 𝜂))
3	2	exp5k 33647	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Syntax hints:   → wi 4   ∧ wa 398

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 209  df-an 399

This theorem is referenced by: (None)