Theorem exp53 600

Description: An exportation inference. (Contributed by Jeff Hankins, 30-Aug-2009.)

Hypothesis

Ref	Expression
exp53.1	⊢ ((((φ ∧ ψ) ∧ (χ ∧ θ)) ∧ τ) → η)

Assertion

Ref	Expression
exp53	⊢ (φ → (ψ → (χ → (θ → (τ → η)))))

Proof of Theorem exp53

Step	Hyp	Ref	Expression
1		exp53.1	. . 3 ⊢ ((((φ ∧ ψ) ∧ (χ ∧ θ)) ∧ τ) → η)
2	1	ex 423	. 2 ⊢ (((φ ∧ ψ) ∧ (χ ∧ θ)) → (τ → η))
3	2	exp43 595	1 ⊢ (φ → (ψ → (χ → (θ → (τ → η)))))

Syntax hints:   → wi 4   ∧ wa 358

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 177  df-an 360

This theorem is referenced by: (None)