Theorem exp5g 34419

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

Hypothesis

Ref	Expression
exp5g.1	⊢ ((𝜑 ∧ 𝜓) → (((𝜒 ∧ 𝜃) ∧ 𝜏) → 𝜂))

Assertion

Ref	Expression
exp5g	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Proof of Theorem exp5g

Step	Hyp	Ref	Expression
1		exp5g.1	. . 3 ⊢ ((𝜑 ∧ 𝜓) → (((𝜒 ∧ 𝜃) ∧ 𝜏) → 𝜂))
2	1	exp4c 432	. 2 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → (𝜃 → (𝜏 → 𝜂))))
3	2	ex 412	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Syntax hints:   → wi 4   ∧ wa 395

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 206  df-an 396

This theorem is referenced by:  exp58  34422