Theorem imp5a 622

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

Hypothesis

Ref	Expression
imp5.1	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Assertion

Ref	Expression
imp5a	⊢ (𝜑 → (𝜓 → (𝜒 → ((𝜃 ∧ 𝜏) → 𝜂))))

Proof of Theorem imp5a

Step	Hyp	Ref	Expression
1		imp5.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))
2		pm3.31 460	. 2 ⊢ ((𝜃 → (𝜏 → 𝜂)) → ((𝜃 ∧ 𝜏) → 𝜂))
3	1, 2	syl8 74	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:  prtlem17  33179  tendospcanN  35330