Theorem exp520 1172

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

Hypothesis

Ref	Expression
exp520.1	⊢ (((φ ∧ ψ ∧ χ) ∧ (θ ∧ τ)) → η)

Assertion

Ref	Expression
exp520	⊢ (φ → (ψ → (χ → (θ → (τ → η)))))

Proof of Theorem exp520

Step	Hyp	Ref	Expression
1		exp520.1	. . 3 ⊢ (((φ ∧ ψ ∧ χ) ∧ (θ ∧ τ)) → η)
2	1	ex 423	. 2 ⊢ ((φ ∧ ψ ∧ χ) → ((θ ∧ τ) → η))
3	2	exp5o 1170	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)