Theorem exp516 1171

Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Hypothesis

Ref	Expression
exp516.1	⊢ (((φ ∧ (ψ ∧ χ ∧ θ)) ∧ τ) → η)

Assertion

Ref	Expression
exp516	⊢ (φ → (ψ → (χ → (θ → (τ → η)))))

Proof of Theorem exp516

Step	Hyp	Ref	Expression
1		exp516.1	. . 3 ⊢ (((φ ∧ (ψ ∧ χ ∧ θ)) ∧ τ) → η)
2	1	exp31 587	. 2 ⊢ (φ → ((ψ ∧ χ ∧ θ) → (τ → η)))
3	2	3expd 1168	1 ⊢ (φ → (ψ → (χ → (θ → (τ → η)))))

This proof depends on syntax axioms:   → wi 4   ∧ wa 358   ∧ w3a 934

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is used by: (None)