Theorem exp5o 1170

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

Hypothesis

Ref	Expression
exp5o.1	⊢ ((φ ∧ ψ ∧ χ) → ((θ ∧ τ) → η))

Assertion

Ref	Expression
exp5o	⊢ (φ → (ψ → (χ → (θ → (τ → η)))))

Proof of Theorem exp5o

Step	Hyp	Ref	Expression
1		exp5o.1	. . 3 ⊢ ((φ ∧ ψ ∧ χ) → ((θ ∧ τ) → η))
2	1	exp3a 425	. 2 ⊢ ((φ ∧ ψ ∧ χ) → (θ → (τ → η)))
3	2	3exp 1150	1 ⊢ (φ → (ψ → (χ → (θ → (τ → η)))))

Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934

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  df-3an 936

This theorem is referenced by:  exp520  1172