Theorem exp5k 31468

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

Hypothesis

Ref	Expression
exp5k.1	⊢ (𝜑 → (((𝜓 ∧ (𝜒 ∧ 𝜃)) ∧ 𝜏) → 𝜂))

Assertion

Ref	Expression
exp5k	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Proof of Theorem exp5k

Step	Hyp	Ref	Expression
1		exp5k.1	. . 3 ⊢ (𝜑 → (((𝜓 ∧ (𝜒 ∧ 𝜃)) ∧ 𝜏) → 𝜂))
2	1	expd 451	. 2 ⊢ (𝜑 → ((𝜓 ∧ (𝜒 ∧ 𝜃)) → (𝜏 → 𝜂)))
3	2	exp4d 635	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Syntax hints:   → wi 4   ∧ wa 383

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 196  df-an 385

This theorem is referenced by:  exp511  31472